Details

analyze884.0ms (5%)

Algorithm

1×	search
2×	egg-herbie

Rules

532×	`associate-l_binary64_23207`
484×	`cancel-sign-sub-inv_binary64_23232`
479×	`distribute-rgt-in_binary64_23216`
427×	`associate-r_binary64_23206`
418×	`neg-sub0_binary64_23261`
386×	`neg-mul-1_binary64_23262`
354×	`distribute-lft-in_binary64_23215`
306×	`*-commutative_binary64_23197`
264×	`unsub-neg_binary64_23260`
208×	`sub-neg_binary64_23259`
176×	`distribute-rgt-neg-out_binary64_23226`
168×	`distribute-lft-neg-out_binary64_23225`
152×	`unswap-sqr_binary64_23234`
109×	`distribute-lft-neg-in_binary64_23223`
100×	`distribute-rgt-neg-in_binary64_23224`
80×	`sqr-pow_binary64_23238`
64×	`distribute-rgt-out_binary64_23219`
60×	`associate-+l-_binary64_23201`
56×	`sub0-neg_binary64_23253` `distribute-lft-out_binary64_23217`
52×	`pow-sqr_binary64_23239`
48×	`rem-sqrt-square_binary64_23279` `associate--r+_binary64_23202`
44×	`div-sub_binary64_23271`
40×	`exp-prod_binary64_23318`
35×	`distribute-rgt-out--_binary64_23220`
34×	`+-rgt-identity_binary64_23251`
28×	`distribute-lft-out--_binary64_23218`
26×	`distribute-neg-in_binary64_23227`
24×	`cube-unmult_binary64_23303`
23×	`--rgt-identity_binary64_23252`
22×	`mul0-rgt_binary64_23249` `mul0-lft_binary64_23248`
20×	`associate-/l*_binary64_23211` `+-commutative_binary64_23196`
18×	`mul-1-neg_binary64_23258` `associate-+l+_binary64_23199`
16×	`unpow3_binary64_23332` `exp-diff_binary64_23314` `associate-/l/_binary64_23213`
12×	`exp-sqrt_binary64_23319`
8×	`pow-plus_binary64_23329` `exp-sum_binary64_23312` `/-rgt-identity_binary64_23257` `remove-double-neg_binary64_23254` `associate-*r/_binary64_23208`
6×	`associate--r-_binary64_23205` `associate--l+_binary64_23203` `associate-+r-_binary64_23200` `associate-+r+_binary64_23198`
4×	`exp-lft-sqr_binary64_23321` `prod-exp_binary64_23315` `cube-prod_binary64_23294` `sqr-neg_binary64_23280` `+-lft-identity_binary64_23250` `count-2_binary64_23214` `associate-/r/_binary64_23212`
1×	`1-exp_binary64_23310`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_23529` `erf-erfc_binary64_23528` `erf-odd_binary64_23527` `if-if-and-not_binary64_23526` `if-if-and_binary64_23525` `if-if-or-not_binary64_23524` `if-if-or_binary64_23523` `if-not_binary64_23522` `if-same_binary64_23521` `if-false_binary64_23520` `if-true_binary64_23519` `not-gte_binary64_23518` `not-lte_binary64_23517` `not-gt_binary64_23516` `not-lt_binary64_23515` `gte-same_binary64_23514` `lte-same_binary64_23513` `gt-same_binary64_23512` `lt-same_binary64_23511` `sinh---cosh_binary64_23458` `sinh-+-cosh_binary64_23457` `sinh-cosh_binary64_23456` `tanh-def-c_binary64_23455` `tanh-def-b_binary64_23454` `tanh-def-a_binary64_23453` `cosh-def_binary64_23452` `sinh-def_binary64_23451` `tan-neg_binary64_23398` `cos-neg_binary64_23397` `sin-neg_binary64_23396` `tan-0_binary64_23395` `cos-0_binary64_23394` `sin-0_binary64_23393` `hang-m-tan_binary64_23392` `hang-p-tan_binary64_23391` `hang-m0-tan_binary64_23390` `hang-p0-tan_binary64_23389` `hang-0m-tan_binary64_23388` `hang-0p-tan_binary64_23387` `tan-+PI/2_binary64_23386` `tan-+PI_binary64_23385` `tan-PI_binary64_23384` `tan-PI/3_binary64_23383` `tan-PI/4_binary64_23382` `tan-PI/6_binary64_23381` `cos-+PI/2_binary64_23380` `cos-+PI_binary64_23379` `cos-PI_binary64_23378` `cos-PI/2_binary64_23377` `cos-PI/3_binary64_23376` `cos-PI/4_binary64_23375` `cos-PI/6_binary64_23374` `sin-+PI/2_binary64_23373` `sin-+PI_binary64_23372` `sin-PI_binary64_23371` `sin-PI/2_binary64_23370` `sin-PI/3_binary64_23369` `sin-PI/4_binary64_23368` `sin-PI/6_binary64_23367` `sub-1-sin_binary64_23366` `sub-1-cos_binary64_23365` `-1-add-sin_binary64_23364` `-1-add-cos_binary64_23363` `1-sub-sin_binary64_23362` `1-sub-cos_binary64_23361` `cos-sin-sum_binary64_23360` `log-E_binary64_23356` `log-pow_binary64_23355` `log-rec_binary64_23354` `log-div_binary64_23353` `log-prod_binary64_23352` `pow-base-0_binary64_23350` `unpow1/3_binary64_23333` `unpow2_binary64_23331` `unpow1/2_binary64_23330` `exp-to-pow_binary64_23328` `pow-base-1_binary64_23326` `unpow0_binary64_23325` `unpow1_binary64_23324` `unpow-1_binary64_23323` `exp-lft-cube_binary64_23322` `exp-cbrt_binary64_23320` `div-exp_binary64_23317` `rec-exp_binary64_23316` `exp-neg_binary64_23313` `e-exp-1_binary64_23311` `exp-1-e_binary64_23309` `exp-0_binary64_23308` `rem-log-exp_binary64_23307` `rem-exp-log_binary64_23306` `cube-mult_binary64_23296` `cube-div_binary64_23295` `cube-neg_binary64_23293` `rem-3cbrt-rft_binary64_23292` `rem-3cbrt-lft_binary64_23291` `rem-cbrt-cube_binary64_23290` `rem-cube-cbrt_binary64_23289` `sqr-abs_binary64_23281` `rem-square-sqrt_binary64_23278` `times-frac_binary64_23272` `-rgt-identity_binary64_23256` `-lft-identity_binary64_23255` `div0_binary64_23247` `-inverses_binary64_23246` `+-inverses_binary64_23245` `lft-mult-inverse_binary64_23244` `rgt-mult-inverse_binary64_23243` `remove-double-div_binary64_23242` `difference-of-sqr--1_binary64_23237` `difference-of-sqr-1_binary64_23236` `difference-of-squares_binary64_23235` `swap-sqr_binary64_23233` `cancel-sign-sub_binary64_23231` `distribute-neg-frac_binary64_23230` `distribute-frac-neg_binary64_23229` `distribute-neg-out_binary64_23228` `distribute-rgt1-in_binary64_23222` `distribute-lft1-in_binary64_23221` `associate-/r_binary64_23210` `associate-*l/_binary64_23209` `associate--l-_binary64_23204`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	175
1	112	175
2	223	175
3	501	175
4	1027	175
5	2117	175
6	3840	175
7	4746	175
8	4942	175
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	74.9%	25.1%	8
6.2%	68.6%	25.1%	9
7.8%	67.1%	25.1%	10
10.1%	64.7%	25.1%	11
14.8%	47.6%	37.6%	12
15.8%	36.8%	47.4%	13
16.6%	35.1%	48.3%	14

Compiler

Compiled 18 to 17 computations (5.6% saved)

sample61.0ms (0.3%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
11.0ms	210×	body	128	invalid
8.0ms	150×	body	128	nan

Compiler

Compiled 35 to 37 computations (-5.7% saved)

simplify171.0ms (1%)

Algorithm

1×	egg-herbie

Rules

814×	`unswap-sqr_binary64_23234`
767×	`cancel-sign-sub-inv_binary64_23232`
435×	`times-frac_binary64_23272`
375×	`*-commutative_binary64_23197`
373×	`neg-sub0_binary64_23261`
367×	`neg-mul-1_binary64_23262`
354×	`exp-prod_binary64_23318`
317×	`distribute-rgt-neg-out_binary64_23226`
316×	`associate-l_binary64_23207`
313×	`distribute-rgt-neg-in_binary64_23224`
289×	`associate-/l/_binary64_23213`
281×	`rem-sqrt-square_binary64_23279`
267×	`sqr-pow_binary64_23238`
260×	`distribute-lft-neg-in_binary64_23223`
256×	`unsub-neg_binary64_23260`
243×	`distribute-rgt-in_binary64_23216`
216×	`distribute-lft-neg-out_binary64_23225`
212×	`associate-r_binary64_23206`
208×	`distribute-lft-in_binary64_23215`
188×	`pow-sqr_binary64_23239`
185×	`distribute-neg-in_binary64_23227`
175×	`remove-double-neg_binary64_23254`
162×	`prod-exp_binary64_23315`
155×	`sub-neg_binary64_23259`
101×	`cancel-sign-sub_binary64_23231`
92×	`cube-prod_binary64_23294`
91×	`distribute-rgt-out_binary64_23219`
81×	`distribute-rgt-out--_binary64_23220`
65×	`associate--r+_binary64_23202`
38×	`unpow3_binary64_23332` `pow-plus_binary64_23329`
34×	`+-lft-identity_binary64_23250` `associate-/l*_binary64_23211`
32×	`cube-mult_binary64_23296`
31×	`+-commutative_binary64_23196`
28×	`distribute-lft-out_binary64_23217`
25×	`distribute-neg-out_binary64_23228` `associate-*l/_binary64_23209` `associate-+l-_binary64_23201`
22×	`mul0-rgt_binary64_23249` `mul0-lft_binary64_23248`
21×	`associate-*r/_binary64_23208`
20×	`sub0-neg_binary64_23253`
19×	`exp-lft-sqr_binary64_23321` `*-lft-identity_binary64_23255`
18×	`distribute-lft-out--_binary64_23218` `associate-/r/_binary64_23212`
16×	`unpow1_binary64_23324` `exp-sqrt_binary64_23319` `remove-double-div_binary64_23242`
14×	`unpow1/2_binary64_23330`
12×	`cube-unmult_binary64_23303`
10×	`unpow2_binary64_23331`
9×	`--rgt-identity_binary64_23252`
7×	`/-rgt-identity_binary64_23257` `*-rgt-identity_binary64_23256` `distribute-rgt1-in_binary64_23222` `associate--r-_binary64_23205` `associate-+r-_binary64_23200`
6×	`mul-1-neg_binary64_23258` `swap-sqr_binary64_23233`
5×	`rem-square-sqrt_binary64_23278` `count-2_binary64_23214`
4×	`+-rgt-identity_binary64_23251` `associate-/r*_binary64_23210` `associate--l+_binary64_23203`
3×	`associate-+l+_binary64_23199`
1×	`1-exp_binary64_23310` `exp-1-e_binary64_23309` `distribute-lft1-in_binary64_23221` `associate-+r+_binary64_23198`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_23529` `erf-erfc_binary64_23528` `erf-odd_binary64_23527` `if-if-and-not_binary64_23526` `if-if-and_binary64_23525` `if-if-or-not_binary64_23524` `if-if-or_binary64_23523` `if-not_binary64_23522` `if-same_binary64_23521` `if-false_binary64_23520` `if-true_binary64_23519` `not-gte_binary64_23518` `not-lte_binary64_23517` `not-gt_binary64_23516` `not-lt_binary64_23515` `gte-same_binary64_23514` `lte-same_binary64_23513` `gt-same_binary64_23512` `lt-same_binary64_23511` `sinh---cosh_binary64_23458` `sinh-+-cosh_binary64_23457` `sinh-cosh_binary64_23456` `tanh-def-c_binary64_23455` `tanh-def-b_binary64_23454` `tanh-def-a_binary64_23453` `cosh-def_binary64_23452` `sinh-def_binary64_23451` `tan-neg_binary64_23398` `cos-neg_binary64_23397` `sin-neg_binary64_23396` `tan-0_binary64_23395` `cos-0_binary64_23394` `sin-0_binary64_23393` `hang-m-tan_binary64_23392` `hang-p-tan_binary64_23391` `hang-m0-tan_binary64_23390` `hang-p0-tan_binary64_23389` `hang-0m-tan_binary64_23388` `hang-0p-tan_binary64_23387` `tan-+PI/2_binary64_23386` `tan-+PI_binary64_23385` `tan-PI_binary64_23384` `tan-PI/3_binary64_23383` `tan-PI/4_binary64_23382` `tan-PI/6_binary64_23381` `cos-+PI/2_binary64_23380` `cos-+PI_binary64_23379` `cos-PI_binary64_23378` `cos-PI/2_binary64_23377` `cos-PI/3_binary64_23376` `cos-PI/4_binary64_23375` `cos-PI/6_binary64_23374` `sin-+PI/2_binary64_23373` `sin-+PI_binary64_23372` `sin-PI_binary64_23371` `sin-PI/2_binary64_23370` `sin-PI/3_binary64_23369` `sin-PI/4_binary64_23368` `sin-PI/6_binary64_23367` `sub-1-sin_binary64_23366` `sub-1-cos_binary64_23365` `-1-add-sin_binary64_23364` `-1-add-cos_binary64_23363` `1-sub-sin_binary64_23362` `1-sub-cos_binary64_23361` `cos-sin-sum_binary64_23360` `log-E_binary64_23356` `log-pow_binary64_23355` `log-rec_binary64_23354` `log-div_binary64_23353` `log-prod_binary64_23352` `pow-base-0_binary64_23350` `unpow1/3_binary64_23333` `exp-to-pow_binary64_23328` `pow-base-1_binary64_23326` `unpow0_binary64_23325` `unpow-1_binary64_23323` `exp-lft-cube_binary64_23322` `exp-cbrt_binary64_23320` `div-exp_binary64_23317` `rec-exp_binary64_23316` `exp-diff_binary64_23314` `exp-neg_binary64_23313` `exp-sum_binary64_23312` `e-exp-1_binary64_23311` `exp-0_binary64_23308` `rem-log-exp_binary64_23307` `rem-exp-log_binary64_23306` `cube-div_binary64_23295` `cube-neg_binary64_23293` `rem-3cbrt-rft_binary64_23292` `rem-3cbrt-lft_binary64_23291` `rem-cbrt-cube_binary64_23290` `rem-cube-cbrt_binary64_23289` `sqr-abs_binary64_23281` `sqr-neg_binary64_23280` `div-sub_binary64_23271` `div0_binary64_23247` `*-inverses_binary64_23246` `+-inverses_binary64_23245` `lft-mult-inverse_binary64_23244` `rgt-mult-inverse_binary64_23243` `difference-of-sqr--1_binary64_23237` `difference-of-sqr-1_binary64_23236` `difference-of-squares_binary64_23235` `distribute-neg-frac_binary64_23230` `distribute-frac-neg_binary64_23229` `associate--l-_binary64_23204`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	28	25
2	49	25
3	97	25
4	193	25
5	396	25
6	1054	25
7	1820	25
8	2881	25
9	4392	25
10	4981	25
11	4311	25
12	4496	25
13	3273	25
14	4672	25
15	4928	25
16	4864	25

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.3b

Counts

2 → 1

Compiler

Compiled 32 to 30 computations (6.3% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 t))
0.0b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

rewrite334.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`add-exp-log_binary64_23304`
14×	`associate-r_binary64_23206`
13×	`add-sqr-sqrt_binary64_23288`
10×	`prod-exp_binary64_23315` `add-cbrt-cube_binary64_23302` `add-cube-cbrt_binary64_23301` `*-un-lft-identity_binary64_23266`
7×	`sqrt-prod_binary64_23282`
6×	`pow1_binary64_23327` `associate-*l/_binary64_23209` `unpow-prod-down_binary64_23345`
4×	`cbrt-unprod_binary64_23299` `associate-l_binary64_23207` `sqrt-pow1_binary64_23284`
3×	`add-log-exp_binary64_23305` `exp-prod_binary64_23318`
2×	`flip3--_binary64_23270` `flip--_binary64_23241` `*-commutative_binary64_23197` `pow-to-exp_binary64_23335` `pow-exp_binary64_23334`
1×	`pow-prod-down_binary64_23337` `unswap-sqr_binary64_23234` `sqr-pow_binary64_23238` `pow1/2_binary64_23346` `rem-sqrt-square_binary64_23279`

Counts

3 → 66

Calls

3 calls:

218.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
10.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
2.0ms	(sqrt.f64 (exp.f64 t))

Compiler

Compiled 1633 to 911 computations (44.2% saved)

series1.4s (7.9%)

Error

0.2b

Counts

3 → 41

Calls

3 calls:

994.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
331.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
33.0ms	(sqrt.f64 (exp.f64 t))

Compiler

Compiled 2613 to 1885 computations (27.9% saved)

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

295×	`associate-l_binary64_23207`
290×	`associate-r_binary64_23206`
253×	`distribute-rgt-in_binary64_23216`
251×	`distribute-lft-in_binary64_23215`
227×	`cancel-sign-sub-inv_binary64_23232`
203×	`distribute-lft-neg-out_binary64_23225`
195×	`sub-neg_binary64_23259`
182×	`distribute-rgt-neg-out_binary64_23226`
156×	`*-commutative_binary64_23197`
113×	`sqr-pow_binary64_23238`
99×	`neg-sub0_binary64_23261`
98×	`neg-mul-1_binary64_23262`
97×	`distribute-rgt-neg-in_binary64_23224`
92×	`unswap-sqr_binary64_23234`
83×	`unsub-neg_binary64_23260`
81×	`distribute-lft-neg-in_binary64_23223`
72×	`+-commutative_binary64_23196`
67×	`exp-prod_binary64_23318`
65×	`associate-+l+_binary64_23199`
57×	`*-lft-identity_binary64_23255`
54×	`log-prod_binary64_23352`
53×	`associate--l+_binary64_23203`
52×	`distribute-rgt-out_binary64_23219`
49×	`*-rgt-identity_binary64_23256` `associate--r+_binary64_23202`
46×	`cube-prod_binary64_23294` `associate-+r+_binary64_23198`
42×	`swap-sqr_binary64_23233`
37×	`exp-sum_binary64_23312`
35×	`pow-sqr_binary64_23239`
24×	`distribute-lft-out_binary64_23217`
21×	`associate-+l-_binary64_23201`
20×	`distribute-rgt-out--_binary64_23220` `associate-+r-_binary64_23200`
18×	`+-rgt-identity_binary64_23251` `distribute-neg-in_binary64_23227`
17×	`distribute-lft-out--_binary64_23218`
12×	`unpow3_binary64_23332` `sub0-neg_binary64_23253`
10×	`cube-unmult_binary64_23303`
8×	`log-pow_binary64_23355` `cube-mult_binary64_23296` `associate-/l*_binary64_23211`
6×	`difference-of-squares_binary64_23235`
5×	`rem-sqrt-square_binary64_23279`
4×	`unpow1/2_binary64_23330` `pow-base-1_binary64_23326` `exp-diff_binary64_23314` `exp-neg_binary64_23313` `distribute-rgt1-in_binary64_23222`
3×	`sqr-neg_binary64_23280` `div-sub_binary64_23271` `cancel-sign-sub_binary64_23231` `associate-/l/_binary64_23213` `associate-*r/_binary64_23208`
2×	`rem-square-sqrt_binary64_23278` `mul-1-neg_binary64_23258` `distribute-lft1-in_binary64_23221` `associate--l-_binary64_23204`
1×	`unpow2_binary64_23331` `pow-plus_binary64_23329` `unpow1_binary64_23324` `1-exp_binary64_23310` `exp-1-e_binary64_23309` `/-rgt-identity_binary64_23257` `count-2_binary64_23214`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_23529` `erf-erfc_binary64_23528` `erf-odd_binary64_23527` `if-if-and-not_binary64_23526` `if-if-and_binary64_23525` `if-if-or-not_binary64_23524` `if-if-or_binary64_23523` `if-not_binary64_23522` `if-same_binary64_23521` `if-false_binary64_23520` `if-true_binary64_23519` `not-gte_binary64_23518` `not-lte_binary64_23517` `not-gt_binary64_23516` `not-lt_binary64_23515` `gte-same_binary64_23514` `lte-same_binary64_23513` `gt-same_binary64_23512` `lt-same_binary64_23511` `sinh---cosh_binary64_23458` `sinh-+-cosh_binary64_23457` `sinh-cosh_binary64_23456` `tanh-def-c_binary64_23455` `tanh-def-b_binary64_23454` `tanh-def-a_binary64_23453` `cosh-def_binary64_23452` `sinh-def_binary64_23451` `tan-neg_binary64_23398` `cos-neg_binary64_23397` `sin-neg_binary64_23396` `tan-0_binary64_23395` `cos-0_binary64_23394` `sin-0_binary64_23393` `hang-m-tan_binary64_23392` `hang-p-tan_binary64_23391` `hang-m0-tan_binary64_23390` `hang-p0-tan_binary64_23389` `hang-0m-tan_binary64_23388` `hang-0p-tan_binary64_23387` `tan-+PI/2_binary64_23386` `tan-+PI_binary64_23385` `tan-PI_binary64_23384` `tan-PI/3_binary64_23383` `tan-PI/4_binary64_23382` `tan-PI/6_binary64_23381` `cos-+PI/2_binary64_23380` `cos-+PI_binary64_23379` `cos-PI_binary64_23378` `cos-PI/2_binary64_23377` `cos-PI/3_binary64_23376` `cos-PI/4_binary64_23375` `cos-PI/6_binary64_23374` `sin-+PI/2_binary64_23373` `sin-+PI_binary64_23372` `sin-PI_binary64_23371` `sin-PI/2_binary64_23370` `sin-PI/3_binary64_23369` `sin-PI/4_binary64_23368` `sin-PI/6_binary64_23367` `sub-1-sin_binary64_23366` `sub-1-cos_binary64_23365` `-1-add-sin_binary64_23364` `-1-add-cos_binary64_23363` `1-sub-sin_binary64_23362` `1-sub-cos_binary64_23361` `cos-sin-sum_binary64_23360` `log-E_binary64_23356` `log-rec_binary64_23354` `log-div_binary64_23353` `pow-base-0_binary64_23350` `unpow1/3_binary64_23333` `exp-to-pow_binary64_23328` `unpow0_binary64_23325` `unpow-1_binary64_23323` `exp-lft-cube_binary64_23322` `exp-lft-sqr_binary64_23321` `exp-cbrt_binary64_23320` `exp-sqrt_binary64_23319` `div-exp_binary64_23317` `rec-exp_binary64_23316` `prod-exp_binary64_23315` `e-exp-1_binary64_23311` `exp-0_binary64_23308` `rem-log-exp_binary64_23307` `rem-exp-log_binary64_23306` `cube-div_binary64_23295` `cube-neg_binary64_23293` `rem-3cbrt-rft_binary64_23292` `rem-3cbrt-lft_binary64_23291` `rem-cbrt-cube_binary64_23290` `rem-cube-cbrt_binary64_23289` `sqr-abs_binary64_23281` `times-frac_binary64_23272` `remove-double-neg_binary64_23254` `--rgt-identity_binary64_23252` `+-lft-identity_binary64_23250` `mul0-rgt_binary64_23249` `mul0-lft_binary64_23248` `div0_binary64_23247` `-inverses_binary64_23246` `+-inverses_binary64_23245` `lft-mult-inverse_binary64_23244` `rgt-mult-inverse_binary64_23243` `remove-double-div_binary64_23242` `difference-of-sqr--1_binary64_23237` `difference-of-sqr-1_binary64_23236` `distribute-neg-frac_binary64_23230` `distribute-frac-neg_binary64_23229` `distribute-neg-out_binary64_23228` `associate-/r/_binary64_23212` `associate-/r_binary64_23210` `associate-*l/_binary64_23209` `associate--r-_binary64_23205`

Counts

107 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	186	2636
1	484	2391
2	1671	2116
3	3733	2111
4	5013	2111

prune131.0ms (0.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	75	11	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	12	87

Error

0.0b

Counts

87 → 12

Compiler

Compiled 2063 to 1215 computations (41.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 t))
0.0b	(.f64 (.f64 (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b	(.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))
0.5b	(.f64 (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)) (sqrt.f64 2))

rewrite203.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

35×	`add-exp-log_binary64_23304`
22×	`prod-exp_binary64_23315`
21×	`add-sqr-sqrt_binary64_23288`
20×	`add-cbrt-cube_binary64_23302`
19×	`associate-r_binary64_23206`
16×	`add-cube-cbrt_binary64_23301` `*-un-lft-identity_binary64_23266`
13×	`sqrt-prod_binary64_23282`
12×	`pow1_binary64_23327`
10×	`cbrt-unprod_binary64_23299`
8×	`associate-l_binary64_23207`
6×	`associate-r/_binary64_23208` `associate-l/_binary64_23209` `cancel-sign-sub-inv_binary64_23232` `unpow-prod-down_binary64_23345`
4×	`pow-prod-down_binary64_23337` `add-log-exp_binary64_23305` `distribute-rgt-in_binary64_23216` `distribute-lft-in_binary64_23215` `sqrt-pow1_binary64_23284`
3×	`flip3--_binary64_23270` `flip--_binary64_23241` `*-commutative_binary64_23197` `pow-to-exp_binary64_23335` `pow-exp_binary64_23334` `exp-prod_binary64_23318`
2×	`unswap-sqr_binary64_23234` `sub-neg_binary64_23259`
1×	`sqr-pow_binary64_23238` `pow1/2_binary64_23346` `rem-sqrt-square_binary64_23279`

Counts

4 → 104

Calls

4 calls:

16.0ms	(.f64 (.f64 (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
11.0ms	(.f64 (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)) (sqrt.f64 2))
9.0ms	(.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))
2.0ms	(sqrt.f64 (exp.f64 t))

Compiler

Compiled 2671 to 1389 computations (48% saved)

series1.7s (9.7%)

Error

0.0b

Counts

4 → 56

Calls

4 calls:

1.0s	(.f64 (.f64 (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
375.0ms	(.f64 (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)) (sqrt.f64 2))
236.0ms	(.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))
28.0ms	(sqrt.f64 (exp.f64 t))

Compiler

Compiled 3443 to 2486 computations (27.8% saved)

simplify169.0ms (1%)

Algorithm

1×	egg-herbie

Rules

518×	`associate-l_binary64_23207`
436×	`associate-r_binary64_23206`
372×	`distribute-rgt-in_binary64_23216`
368×	`distribute-lft-in_binary64_23215`
241×	`cancel-sign-sub-inv_binary64_23232`
214×	`*-commutative_binary64_23197`
184×	`exp-prod_binary64_23318`
135×	`log-prod_binary64_23352`
104×	`distribute-rgt-neg-in_binary64_23224`
83×	`distribute-lft-neg-in_binary64_23223`
67×	`sqr-pow_binary64_23238`
61×	`sub-neg_binary64_23259` `distribute-rgt-out_binary64_23219`
54×	`swap-sqr_binary64_23233`
50×	`*-lft-identity_binary64_23255`
44×	`cube-prod_binary64_23294` `+-commutative_binary64_23196`
43×	`*-rgt-identity_binary64_23256`
41×	`distribute-lft-neg-out_binary64_23225`
38×	`unswap-sqr_binary64_23234`
33×	`neg-sub0_binary64_23261`
32×	`distribute-rgt-neg-out_binary64_23226`
30×	`neg-mul-1_binary64_23262`
25×	`unpow3_binary64_23332` `distribute-rgt-out--_binary64_23220` `associate-+l+_binary64_23199`
24×	`distribute-lft-out_binary64_23217`
18×	`associate-+r+_binary64_23198`
16×	`pow-sqr_binary64_23239` `distribute-lft-out--_binary64_23218`
14×	`exp-diff_binary64_23314`
12×	`distribute-neg-in_binary64_23227` `associate--l+_binary64_23203` `associate--r+_binary64_23202`
11×	`log-pow_binary64_23355` `unsub-neg_binary64_23260`
10×	`cube-unmult_binary64_23303`
7×	`unpow1/2_binary64_23330` `rem-sqrt-square_binary64_23279`
6×	`exp-sum_binary64_23312`
4×	`pow-plus_binary64_23329` `pow-base-1_binary64_23326` `cube-mult_binary64_23296` `rem-square-sqrt_binary64_23278` `distribute-rgt1-in_binary64_23222`
3×	`mul-1-neg_binary64_23258` `difference-of-squares_binary64_23235`
2×	`div-sub_binary64_23271` `distribute-lft1-in_binary64_23221`
1×	`unpow2_binary64_23331` `unpow1_binary64_23324` `1-exp_binary64_23310` `exp-1-e_binary64_23309` `rem-3cbrt-lft_binary64_23291` `+-rgt-identity_binary64_23251` `associate-/l/_binary64_23213` `associate-+r-_binary64_23200`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_23529` `erf-erfc_binary64_23528` `erf-odd_binary64_23527` `if-if-and-not_binary64_23526` `if-if-and_binary64_23525` `if-if-or-not_binary64_23524` `if-if-or_binary64_23523` `if-not_binary64_23522` `if-same_binary64_23521` `if-false_binary64_23520` `if-true_binary64_23519` `not-gte_binary64_23518` `not-lte_binary64_23517` `not-gt_binary64_23516` `not-lt_binary64_23515` `gte-same_binary64_23514` `lte-same_binary64_23513` `gt-same_binary64_23512` `lt-same_binary64_23511` `sinh---cosh_binary64_23458` `sinh-+-cosh_binary64_23457` `sinh-cosh_binary64_23456` `tanh-def-c_binary64_23455` `tanh-def-b_binary64_23454` `tanh-def-a_binary64_23453` `cosh-def_binary64_23452` `sinh-def_binary64_23451` `tan-neg_binary64_23398` `cos-neg_binary64_23397` `sin-neg_binary64_23396` `tan-0_binary64_23395` `cos-0_binary64_23394` `sin-0_binary64_23393` `hang-m-tan_binary64_23392` `hang-p-tan_binary64_23391` `hang-m0-tan_binary64_23390` `hang-p0-tan_binary64_23389` `hang-0m-tan_binary64_23388` `hang-0p-tan_binary64_23387` `tan-+PI/2_binary64_23386` `tan-+PI_binary64_23385` `tan-PI_binary64_23384` `tan-PI/3_binary64_23383` `tan-PI/4_binary64_23382` `tan-PI/6_binary64_23381` `cos-+PI/2_binary64_23380` `cos-+PI_binary64_23379` `cos-PI_binary64_23378` `cos-PI/2_binary64_23377` `cos-PI/3_binary64_23376` `cos-PI/4_binary64_23375` `cos-PI/6_binary64_23374` `sin-+PI/2_binary64_23373` `sin-+PI_binary64_23372` `sin-PI_binary64_23371` `sin-PI/2_binary64_23370` `sin-PI/3_binary64_23369` `sin-PI/4_binary64_23368` `sin-PI/6_binary64_23367` `sub-1-sin_binary64_23366` `sub-1-cos_binary64_23365` `-1-add-sin_binary64_23364` `-1-add-cos_binary64_23363` `1-sub-sin_binary64_23362` `1-sub-cos_binary64_23361` `cos-sin-sum_binary64_23360` `log-E_binary64_23356` `log-rec_binary64_23354` `log-div_binary64_23353` `pow-base-0_binary64_23350` `unpow1/3_binary64_23333` `exp-to-pow_binary64_23328` `unpow0_binary64_23325` `unpow-1_binary64_23323` `exp-lft-cube_binary64_23322` `exp-lft-sqr_binary64_23321` `exp-cbrt_binary64_23320` `exp-sqrt_binary64_23319` `div-exp_binary64_23317` `rec-exp_binary64_23316` `prod-exp_binary64_23315` `exp-neg_binary64_23313` `e-exp-1_binary64_23311` `exp-0_binary64_23308` `rem-log-exp_binary64_23307` `rem-exp-log_binary64_23306` `cube-div_binary64_23295` `cube-neg_binary64_23293` `rem-3cbrt-rft_binary64_23292` `rem-cbrt-cube_binary64_23290` `rem-cube-cbrt_binary64_23289` `sqr-abs_binary64_23281` `sqr-neg_binary64_23280` `times-frac_binary64_23272` `/-rgt-identity_binary64_23257` `remove-double-neg_binary64_23254` `sub0-neg_binary64_23253` `--rgt-identity_binary64_23252` `+-lft-identity_binary64_23250` `mul0-rgt_binary64_23249` `mul0-lft_binary64_23248` `div0_binary64_23247` `-inverses_binary64_23246` `+-inverses_binary64_23245` `lft-mult-inverse_binary64_23244` `rgt-mult-inverse_binary64_23243` `remove-double-div_binary64_23242` `difference-of-sqr--1_binary64_23237` `difference-of-sqr-1_binary64_23236` `cancel-sign-sub_binary64_23231` `distribute-neg-frac_binary64_23230` `distribute-frac-neg_binary64_23229` `distribute-neg-out_binary64_23228` `count-2_binary64_23214` `associate-/r/_binary64_23212` `associate-/l_binary64_23211` `associate-/r_binary64_23210` `associate-l/_binary64_23209` `associate-*r/_binary64_23208` `associate--r-_binary64_23205` `associate--l-_binary64_23204` `associate-+l-_binary64_23201`

Counts

160 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	3758
1	603	3334
2	2303	3020
3	4738	3020
4	4979	3020
5	4967	3020

prune159.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	128	8	136

Error

0.0b

Counts

136 → 8

Compiler

Compiled 2722 to 1437 computations (47.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.2b	(.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))

rewrite379.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

87×	`add-exp-log_binary64_23304`
64×	`prod-exp_binary64_23315`
36×	`add-cbrt-cube_binary64_23302`
34×	`cbrt-unprod_binary64_23299`
32×	`pow1_binary64_23327`
21×	`associate-r_binary64_23206`
19×	`pow-prod-down_binary64_23337`
14×	`add-sqr-sqrt_binary64_23288` `associate-*l/_binary64_23209`
13×	`add-cube-cbrt_binary64_23301` `*-un-lft-identity_binary64_23266`
11×	`associate-l_binary64_23207`
9×	`sqrt-prod_binary64_23282`
6×	`associate-*r/_binary64_23208` `cbrt-prod_binary64_23297` `unpow-prod-down_binary64_23345`
5×	`pow-to-exp_binary64_23335` `pow-exp_binary64_23334`
4×	`add-log-exp_binary64_23305` `flip3--_binary64_23270` `flip--_binary64_23241` `*-commutative_binary64_23197`
1×	`unswap-sqr_binary64_23234` `sqr-pow_binary64_23238`

Counts

4 → 120

Calls

4 calls:

29.0ms	(.f64 (.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
20.0ms	(.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
16.0ms	(.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
12.0ms	(.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 4510 to 3020 computations (33% saved)

series3.0s (16.8%)

Error

0.0b

Counts

4 → 62

Calls

4 calls:

1.1s	(.f64 (.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
886.0ms	(.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
583.0ms	(.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
382.0ms	(.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))

Compiler

Compiled 4556 to 3555 computations (22% saved)

simplify145.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-l_binary64_23207`
524×	`associate-r_binary64_23206`
394×	`distribute-rgt-in_binary64_23216`
392×	`distribute-lft-in_binary64_23215`
268×	`*-commutative_binary64_23197`
246×	`cancel-sign-sub-inv_binary64_23232`
113×	`distribute-rgt-neg-in_binary64_23224`
94×	`distribute-lft-neg-in_binary64_23223`
81×	`exp-prod_binary64_23318`
77×	`log-prod_binary64_23352`
70×	`sqr-pow_binary64_23238`
61×	`unswap-sqr_binary64_23234`
60×	`sub-neg_binary64_23259`
59×	`cube-prod_binary64_23294`
58×	`swap-sqr_binary64_23233`
53×	`distribute-rgt-out_binary64_23219`
46×	`+-commutative_binary64_23196`
38×	`distribute-lft-neg-out_binary64_23225`
33×	`associate-+l+_binary64_23199`
30×	`neg-sub0_binary64_23261`
27×	`*-lft-identity_binary64_23255` `distribute-rgt-out--_binary64_23220`
26×	`neg-mul-1_binary64_23262`
22×	`*-rgt-identity_binary64_23256`
20×	`distribute-rgt-neg-out_binary64_23226`
18×	`pow-sqr_binary64_23239`
17×	`distribute-lft-out--_binary64_23218`
16×	`distribute-lft-out_binary64_23217` `associate-+r+_binary64_23198`
13×	`cube-unmult_binary64_23303`
12×	`distribute-neg-in_binary64_23227` `associate--l+_binary64_23203` `associate--r+_binary64_23202`
10×	`unsub-neg_binary64_23260`
8×	`exp-sum_binary64_23312`
5×	`rem-sqrt-square_binary64_23279`
4×	`log-pow_binary64_23355` `mul-1-neg_binary64_23258` `distribute-rgt1-in_binary64_23222`
3×	`unpow3_binary64_23332` `pow-base-1_binary64_23326` `cube-mult_binary64_23296` `difference-of-squares_binary64_23235` `distribute-lft1-in_binary64_23221`
2×	`unpow2_binary64_23331` `unpow1/2_binary64_23330` `pow-plus_binary64_23329` `unpow1_binary64_23324` `exp-diff_binary64_23314` `rem-square-sqrt_binary64_23278`
1×	`unpow1/3_binary64_23333` `1-exp_binary64_23310` `exp-1-e_binary64_23309` `rem-3cbrt-rft_binary64_23292` `rem-3cbrt-lft_binary64_23291` `count-2_binary64_23214` `associate-/l/_binary64_23213`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_23529` `erf-erfc_binary64_23528` `erf-odd_binary64_23527` `if-if-and-not_binary64_23526` `if-if-and_binary64_23525` `if-if-or-not_binary64_23524` `if-if-or_binary64_23523` `if-not_binary64_23522` `if-same_binary64_23521` `if-false_binary64_23520` `if-true_binary64_23519` `not-gte_binary64_23518` `not-lte_binary64_23517` `not-gt_binary64_23516` `not-lt_binary64_23515` `gte-same_binary64_23514` `lte-same_binary64_23513` `gt-same_binary64_23512` `lt-same_binary64_23511` `sinh---cosh_binary64_23458` `sinh-+-cosh_binary64_23457` `sinh-cosh_binary64_23456` `tanh-def-c_binary64_23455` `tanh-def-b_binary64_23454` `tanh-def-a_binary64_23453` `cosh-def_binary64_23452` `sinh-def_binary64_23451` `tan-neg_binary64_23398` `cos-neg_binary64_23397` `sin-neg_binary64_23396` `tan-0_binary64_23395` `cos-0_binary64_23394` `sin-0_binary64_23393` `hang-m-tan_binary64_23392` `hang-p-tan_binary64_23391` `hang-m0-tan_binary64_23390` `hang-p0-tan_binary64_23389` `hang-0m-tan_binary64_23388` `hang-0p-tan_binary64_23387` `tan-+PI/2_binary64_23386` `tan-+PI_binary64_23385` `tan-PI_binary64_23384` `tan-PI/3_binary64_23383` `tan-PI/4_binary64_23382` `tan-PI/6_binary64_23381` `cos-+PI/2_binary64_23380` `cos-+PI_binary64_23379` `cos-PI_binary64_23378` `cos-PI/2_binary64_23377` `cos-PI/3_binary64_23376` `cos-PI/4_binary64_23375` `cos-PI/6_binary64_23374` `sin-+PI/2_binary64_23373` `sin-+PI_binary64_23372` `sin-PI_binary64_23371` `sin-PI/2_binary64_23370` `sin-PI/3_binary64_23369` `sin-PI/4_binary64_23368` `sin-PI/6_binary64_23367` `sub-1-sin_binary64_23366` `sub-1-cos_binary64_23365` `-1-add-sin_binary64_23364` `-1-add-cos_binary64_23363` `1-sub-sin_binary64_23362` `1-sub-cos_binary64_23361` `cos-sin-sum_binary64_23360` `log-E_binary64_23356` `log-rec_binary64_23354` `log-div_binary64_23353` `pow-base-0_binary64_23350` `exp-to-pow_binary64_23328` `unpow0_binary64_23325` `unpow-1_binary64_23323` `exp-lft-cube_binary64_23322` `exp-lft-sqr_binary64_23321` `exp-cbrt_binary64_23320` `exp-sqrt_binary64_23319` `div-exp_binary64_23317` `rec-exp_binary64_23316` `prod-exp_binary64_23315` `exp-neg_binary64_23313` `e-exp-1_binary64_23311` `exp-0_binary64_23308` `rem-log-exp_binary64_23307` `rem-exp-log_binary64_23306` `cube-div_binary64_23295` `cube-neg_binary64_23293` `rem-cbrt-cube_binary64_23290` `rem-cube-cbrt_binary64_23289` `sqr-abs_binary64_23281` `sqr-neg_binary64_23280` `times-frac_binary64_23272` `div-sub_binary64_23271` `/-rgt-identity_binary64_23257` `remove-double-neg_binary64_23254` `sub0-neg_binary64_23253` `--rgt-identity_binary64_23252` `+-rgt-identity_binary64_23251` `+-lft-identity_binary64_23250` `mul0-rgt_binary64_23249` `mul0-lft_binary64_23248` `div0_binary64_23247` `-inverses_binary64_23246` `+-inverses_binary64_23245` `lft-mult-inverse_binary64_23244` `rgt-mult-inverse_binary64_23243` `remove-double-div_binary64_23242` `difference-of-sqr--1_binary64_23237` `difference-of-sqr-1_binary64_23236` `cancel-sign-sub_binary64_23231` `distribute-neg-frac_binary64_23230` `distribute-frac-neg_binary64_23229` `distribute-neg-out_binary64_23228` `associate-/r/_binary64_23212` `associate-/l_binary64_23211` `associate-/r_binary64_23210` `associate-l/_binary64_23209` `associate-*r/_binary64_23208` `associate--r-_binary64_23205` `associate--l-_binary64_23204` `associate-+l-_binary64_23201` `associate-+r-_binary64_23200`

Counts

182 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	6808
1	681	4613
2	2558	4211
3	5378	4211

prune208.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	148	8	156

Error

0.0b

Counts

156 → 8

Compiler

Compiled 3450 to 1984 computations (42.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (*.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.2b	(.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2)))
0.4b	(.f64 (sqrt.f64 z) (.f64 (-.f64 (*.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2))))

rewrite302.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

58×	`add-exp-log_binary64_23304`
40×	`prod-exp_binary64_23315`
34×	`add-cbrt-cube_binary64_23302`
29×	`associate-r_binary64_23206`
27×	`sqrt-prod_binary64_23282`
22×	`add-sqr-sqrt_binary64_23288`
20×	`pow1_binary64_23327` `cbrt-unprod_binary64_23299`
16×	`add-cube-cbrt_binary64_23301` `*-un-lft-identity_binary64_23266`
14×	`associate-*l/_binary64_23209`
11×	`associate-l_binary64_23207`
10×	`pow-prod-down_binary64_23337`
6×	`associate-*r/_binary64_23208` `unpow-prod-down_binary64_23345`
4×	`add-log-exp_binary64_23305` `flip3--_binary64_23270` `flip--_binary64_23241` `*-commutative_binary64_23197` `pow-to-exp_binary64_23335` `pow-exp_binary64_23334`
3×	`unswap-sqr_binary64_23234`
1×	`sqr-pow_binary64_23238`

Counts

4 → 117

Calls

4 calls:

27.0ms	(.f64 (.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (*.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
17.0ms	(.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2)))
12.0ms	(.f64 (sqrt.f64 z) (.f64 (-.f64 (*.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2))))
10.0ms	(.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 3835 to 2422 computations (36.8% saved)

series2.1s (11.5%)

Error

Counts

4 → 62

Calls

4 calls:

1.0s	(.f64 (.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (*.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
376.0ms	(.f64 (sqrt.f64 z) (.f64 (-.f64 (*.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2))))
348.0ms	(.f64 (.f64 (sqrt.f64 z) (.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2)))
232.0ms	(.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 4140 to 3173 computations (23.4% saved)

simplify131.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

599×	`associate-l_binary64_23207`
510×	`associate-r_binary64_23206`
411×	`distribute-rgt-in_binary64_23216`
408×	`distribute-lft-in_binary64_23215`
245×	`cancel-sign-sub-inv_binary64_23232`
232×	`*-commutative_binary64_23197`
108×	`distribute-rgt-neg-in_binary64_23224`
99×	`exp-prod_binary64_23318`
95×	`log-prod_binary64_23352`
91×	`distribute-lft-neg-in_binary64_23223`
73×	`swap-sqr_binary64_23233`
68×	`sqr-pow_binary64_23238`
61×	`sub-neg_binary64_23259`
52×	`cube-prod_binary64_23294`
45×	`distribute-rgt-out_binary64_23219`
40×	`unswap-sqr_binary64_23234`
38×	`+-commutative_binary64_23196`
37×	`distribute-lft-neg-out_binary64_23225`
31×	`neg-sub0_binary64_23261`
28×	`*-lft-identity_binary64_23255`
27×	`neg-mul-1_binary64_23262` `*-rgt-identity_binary64_23256` `associate-+l+_binary64_23199`
22×	`distribute-rgt-neg-out_binary64_23226` `distribute-rgt-out--_binary64_23220`
18×	`pow-sqr_binary64_23239`
17×	`distribute-lft-out--_binary64_23218`
16×	`distribute-lft-out_binary64_23217`
12×	`distribute-neg-in_binary64_23227` `associate--l+_binary64_23203` `associate--r+_binary64_23202` `associate-+r+_binary64_23198`
11×	`cube-unmult_binary64_23303`
10×	`exp-sum_binary64_23312` `unsub-neg_binary64_23260`
8×	`rem-sqrt-square_binary64_23279`
4×	`log-pow_binary64_23355` `mul-1-neg_binary64_23258` `distribute-rgt1-in_binary64_23222`
3×	`unpow3_binary64_23332` `pow-base-1_binary64_23326` `exp-diff_binary64_23314` `cube-mult_binary64_23296` `difference-of-squares_binary64_23235`
2×	`rem-square-sqrt_binary64_23278` `distribute-lft1-in_binary64_23221`
1×	`unpow2_binary64_23331` `unpow1/2_binary64_23330` `pow-plus_binary64_23329` `unpow1_binary64_23324` `1-exp_binary64_23310` `exp-1-e_binary64_23309` `div-sub_binary64_23271` `associate-/l/_binary64_23213`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_23529` `erf-erfc_binary64_23528` `erf-odd_binary64_23527` `if-if-and-not_binary64_23526` `if-if-and_binary64_23525` `if-if-or-not_binary64_23524` `if-if-or_binary64_23523` `if-not_binary64_23522` `if-same_binary64_23521` `if-false_binary64_23520` `if-true_binary64_23519` `not-gte_binary64_23518` `not-lte_binary64_23517` `not-gt_binary64_23516` `not-lt_binary64_23515` `gte-same_binary64_23514` `lte-same_binary64_23513` `gt-same_binary64_23512` `lt-same_binary64_23511` `sinh---cosh_binary64_23458` `sinh-+-cosh_binary64_23457` `sinh-cosh_binary64_23456` `tanh-def-c_binary64_23455` `tanh-def-b_binary64_23454` `tanh-def-a_binary64_23453` `cosh-def_binary64_23452` `sinh-def_binary64_23451` `tan-neg_binary64_23398` `cos-neg_binary64_23397` `sin-neg_binary64_23396` `tan-0_binary64_23395` `cos-0_binary64_23394` `sin-0_binary64_23393` `hang-m-tan_binary64_23392` `hang-p-tan_binary64_23391` `hang-m0-tan_binary64_23390` `hang-p0-tan_binary64_23389` `hang-0m-tan_binary64_23388` `hang-0p-tan_binary64_23387` `tan-+PI/2_binary64_23386` `tan-+PI_binary64_23385` `tan-PI_binary64_23384` `tan-PI/3_binary64_23383` `tan-PI/4_binary64_23382` `tan-PI/6_binary64_23381` `cos-+PI/2_binary64_23380` `cos-+PI_binary64_23379` `cos-PI_binary64_23378` `cos-PI/2_binary64_23377` `cos-PI/3_binary64_23376` `cos-PI/4_binary64_23375` `cos-PI/6_binary64_23374` `sin-+PI/2_binary64_23373` `sin-+PI_binary64_23372` `sin-PI_binary64_23371` `sin-PI/2_binary64_23370` `sin-PI/3_binary64_23369` `sin-PI/4_binary64_23368` `sin-PI/6_binary64_23367` `sub-1-sin_binary64_23366` `sub-1-cos_binary64_23365` `-1-add-sin_binary64_23364` `-1-add-cos_binary64_23363` `1-sub-sin_binary64_23362` `1-sub-cos_binary64_23361` `cos-sin-sum_binary64_23360` `log-E_binary64_23356` `log-rec_binary64_23354` `log-div_binary64_23353` `pow-base-0_binary64_23350` `unpow1/3_binary64_23333` `exp-to-pow_binary64_23328` `unpow0_binary64_23325` `unpow-1_binary64_23323` `exp-lft-cube_binary64_23322` `exp-lft-sqr_binary64_23321` `exp-cbrt_binary64_23320` `exp-sqrt_binary64_23319` `div-exp_binary64_23317` `rec-exp_binary64_23316` `prod-exp_binary64_23315` `exp-neg_binary64_23313` `e-exp-1_binary64_23311` `exp-0_binary64_23308` `rem-log-exp_binary64_23307` `rem-exp-log_binary64_23306` `cube-div_binary64_23295` `cube-neg_binary64_23293` `rem-3cbrt-rft_binary64_23292` `rem-3cbrt-lft_binary64_23291` `rem-cbrt-cube_binary64_23290` `rem-cube-cbrt_binary64_23289` `sqr-abs_binary64_23281` `sqr-neg_binary64_23280` `times-frac_binary64_23272` `/-rgt-identity_binary64_23257` `remove-double-neg_binary64_23254` `sub0-neg_binary64_23253` `--rgt-identity_binary64_23252` `+-rgt-identity_binary64_23251` `+-lft-identity_binary64_23250` `mul0-rgt_binary64_23249` `mul0-lft_binary64_23248` `div0_binary64_23247` `-inverses_binary64_23246` `+-inverses_binary64_23245` `lft-mult-inverse_binary64_23244` `rgt-mult-inverse_binary64_23243` `remove-double-div_binary64_23242` `difference-of-sqr--1_binary64_23237` `difference-of-sqr-1_binary64_23236` `cancel-sign-sub_binary64_23231` `distribute-neg-frac_binary64_23230` `distribute-frac-neg_binary64_23229` `distribute-neg-out_binary64_23228` `count-2_binary64_23214` `associate-/r/_binary64_23212` `associate-/l_binary64_23211` `associate-/r_binary64_23210` `associate-l/_binary64_23209` `associate-*r/_binary64_23208` `associate--r-_binary64_23205` `associate--l-_binary64_23204` `associate-+l-_binary64_23201` `associate-+r-_binary64_23200`

Counts

179 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	4891
1	633	4181
2	2515	3846
3	5176	3846

prune219.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	158	8	166

Error

Counts

166 → 8

Compiler

Compiled 3654 to 2100 computations (42.5% saved)

regimes2.3s (13.1%)

Accuracy

Total 0.3b remaining (96.6%)

Threshold costs 0.3b (96.6%)

Compiler

Compiled 24151 to 21869 computations (9.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64_23197`
2×	`sub-neg_binary64_23259` `+-commutative_binary64_23196`
1×	`neg-mul-1_binary64_23262` `neg-sub0_binary64_23261`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64_23526` `if-if-and_binary64_23525` `if-if-or-not_binary64_23524` `if-if-or_binary64_23523` `if-not_binary64_23522` `if-same_binary64_23521` `if-false_binary64_23520` `if-true_binary64_23519` `tan-0_binary64_23395` `cos-0_binary64_23394` `sin-0_binary64_23393` `unpow1_binary64_23324` `e-exp-1_binary64_23311` `1-exp_binary64_23310` `exp-1-e_binary64_23309` `exp-0_binary64_23308` `sqr-abs_binary64_23281` `sqr-neg_binary64_23280` `unsub-neg_binary64_23260` `mul-1-neg_binary64_23258` `/-rgt-identity_binary64_23257` `-rgt-identity_binary64_23256` `-lft-identity_binary64_23255` `remove-double-neg_binary64_23254` `sub0-neg_binary64_23253` `--rgt-identity_binary64_23252` `+-rgt-identity_binary64_23251` `+-lft-identity_binary64_23250` `cancel-sign-sub-inv_binary64_23232` `cancel-sign-sub_binary64_23231` `distribute-neg-frac_binary64_23230` `distribute-frac-neg_binary64_23229` `distribute-neg-out_binary64_23228` `distribute-neg-in_binary64_23227` `distribute-rgt-neg-out_binary64_23226` `distribute-lft-neg-out_binary64_23225` `distribute-rgt-neg-in_binary64_23224` `distribute-lft-neg-in_binary64_23223`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	22	25
2	27	25
3	29	25
4	30	25
5	30	25

end0.0ms (0%)

sample3.6s (20.3%)

Algorithm

1×

intervals

Results

452.0ms	8000×	body	128	valid
351.0ms	6214×	body	128	invalid
257.0ms	4619×	body	128	nan

Compiler

Compiled 1870 to 1692 computations (9.5% saved)

Details

analyze884.0ms (5%)

sample61.0ms (0.3%)

simplify171.0ms (1%)

prune5.0ms (0%)

localize12.0ms (0.1%)

rewrite334.0ms (1.9%)

series1.4s (7.9%)

simplify103.0ms (0.6%)

prune131.0ms (0.7%)

localize13.0ms (0.1%)

rewrite203.0ms (1.1%)

series1.7s (9.7%)

simplify169.0ms (1%)

prune159.0ms (0.9%)

localize16.0ms (0.1%)

rewrite379.0ms (2.1%)

series3.0s (16.8%)

simplify145.0ms (0.8%)

prune208.0ms (1.2%)

localize15.0ms (0.1%)

rewrite302.0ms (1.7%)

series2.1s (11.5%)

simplify131.0ms (0.7%)

prune219.0ms (1.2%)

regimes2.3s (13.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.6s (20.3%)

Profiling