Details

analyze60.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
43.7%	40.6%	15.7%	7
56.2%	23.4%	20.4%	8
57.8%	21.1%	21.2%	9
64%	12.5%	23.5%	10
64.8%	10.7%	24.5%	11
67.9%	6.4%	25.7%	12
68.3%	5.4%	26.3%	13
69.9%	3.3%	26.9%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample18.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify148.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64_14331`
6×	`distribute-rgt-out_binary64_14353`
5×	`associate-l_binary64_14341` `associate-r_binary64_14340`
4×	`distribute-rgt-in_binary64_14350`
3×	`distribute-lft-out_binary64_14351`
2×	`distribute-lft-in_binary64_14349` `+-commutative_binary64_14330`
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_14663` `erf-erfc_binary64_14662` `erf-odd_binary64_14661` `if-if-and-not_binary64_14660` `if-if-and_binary64_14659` `if-if-or-not_binary64_14658` `if-if-or_binary64_14657` `if-not_binary64_14656` `if-same_binary64_14655` `if-false_binary64_14654` `if-true_binary64_14653` `not-gte_binary64_14652` `not-lte_binary64_14651` `not-gt_binary64_14650` `not-lt_binary64_14649` `gte-same_binary64_14648` `lte-same_binary64_14647` `gt-same_binary64_14646` `lt-same_binary64_14645` `sinh---cosh_binary64_14592` `sinh-+-cosh_binary64_14591` `sinh-cosh_binary64_14590` `tanh-def-c_binary64_14589` `tanh-def-b_binary64_14588` `tanh-def-a_binary64_14587` `cosh-def_binary64_14586` `sinh-def_binary64_14585` `tan-neg_binary64_14532` `cos-neg_binary64_14531` `sin-neg_binary64_14530` `tan-0_binary64_14529` `cos-0_binary64_14528` `sin-0_binary64_14527` `hang-m-tan_binary64_14526` `hang-p-tan_binary64_14525` `hang-m0-tan_binary64_14524` `hang-p0-tan_binary64_14523` `hang-0m-tan_binary64_14522` `hang-0p-tan_binary64_14521` `tan-+PI/2_binary64_14520` `tan-+PI_binary64_14519` `tan-PI_binary64_14518` `tan-PI/3_binary64_14517` `tan-PI/4_binary64_14516` `tan-PI/6_binary64_14515` `cos-+PI/2_binary64_14514` `cos-+PI_binary64_14513` `cos-PI_binary64_14512` `cos-PI/2_binary64_14511` `cos-PI/3_binary64_14510` `cos-PI/4_binary64_14509` `cos-PI/6_binary64_14508` `sin-+PI/2_binary64_14507` `sin-+PI_binary64_14506` `sin-PI_binary64_14505` `sin-PI/2_binary64_14504` `sin-PI/3_binary64_14503` `sin-PI/4_binary64_14502` `sin-PI/6_binary64_14501` `sub-1-sin_binary64_14500` `sub-1-cos_binary64_14499` `-1-add-sin_binary64_14498` `-1-add-cos_binary64_14497` `1-sub-sin_binary64_14496` `1-sub-cos_binary64_14495` `cos-sin-sum_binary64_14494` `log-E_binary64_14490` `log-pow_binary64_14489` `log-rec_binary64_14488` `log-div_binary64_14487` `log-prod_binary64_14486` `pow-base-0_binary64_14484` `unpow1/3_binary64_14467` `unpow3_binary64_14466` `unpow2_binary64_14465` `unpow1/2_binary64_14464` `pow-plus_binary64_14463` `exp-to-pow_binary64_14462` `pow-base-1_binary64_14460` `unpow0_binary64_14459` `unpow1_binary64_14458` `unpow-1_binary64_14457` `exp-lft-cube_binary64_14456` `exp-lft-sqr_binary64_14455` `exp-cbrt_binary64_14454` `exp-sqrt_binary64_14453` `exp-prod_binary64_14452` `div-exp_binary64_14451` `rec-exp_binary64_14450` `prod-exp_binary64_14449` `exp-diff_binary64_14448` `exp-neg_binary64_14447` `exp-sum_binary64_14446` `e-exp-1_binary64_14445` `1-exp_binary64_14444` `exp-1-e_binary64_14443` `exp-0_binary64_14442` `rem-log-exp_binary64_14441` `rem-exp-log_binary64_14440` `cube-unmult_binary64_14437` `cube-mult_binary64_14430` `cube-div_binary64_14429` `cube-prod_binary64_14428` `cube-neg_binary64_14427` `rem-3cbrt-rft_binary64_14426` `rem-3cbrt-lft_binary64_14425` `rem-cbrt-cube_binary64_14424` `rem-cube-cbrt_binary64_14423` `sqr-abs_binary64_14415` `sqr-neg_binary64_14414` `rem-sqrt-square_binary64_14413` `rem-square-sqrt_binary64_14412` `times-frac_binary64_14406` `div-sub_binary64_14405` `neg-mul-1_binary64_14396` `neg-sub0_binary64_14395` `unsub-neg_binary64_14394` `sub-neg_binary64_14393` `mul-1-neg_binary64_14392` `/-rgt-identity_binary64_14391` `-rgt-identity_binary64_14390` `-lft-identity_binary64_14389` `remove-double-neg_binary64_14388` `sub0-neg_binary64_14387` `--rgt-identity_binary64_14386` `+-rgt-identity_binary64_14385` `+-lft-identity_binary64_14384` `mul0-rgt_binary64_14383` `mul0-lft_binary64_14382` `div0_binary64_14381` `-inverses_binary64_14380` `+-inverses_binary64_14379` `lft-mult-inverse_binary64_14378` `rgt-mult-inverse_binary64_14377` `remove-double-div_binary64_14376` `pow-sqr_binary64_14373` `sqr-pow_binary64_14372` `difference-of-sqr--1_binary64_14371` `difference-of-sqr-1_binary64_14370` `difference-of-squares_binary64_14369` `unswap-sqr_binary64_14368` `swap-sqr_binary64_14367` `cancel-sign-sub-inv_binary64_14366` `cancel-sign-sub_binary64_14365` `distribute-neg-frac_binary64_14364` `distribute-frac-neg_binary64_14363` `distribute-neg-out_binary64_14362` `distribute-neg-in_binary64_14361` `distribute-rgt-neg-out_binary64_14360` `distribute-lft-neg-out_binary64_14359` `distribute-rgt-neg-in_binary64_14358` `distribute-lft-neg-in_binary64_14357` `distribute-rgt1-in_binary64_14356` `distribute-lft1-in_binary64_14355` `distribute-rgt-out--_binary64_14354` `distribute-lft-out--_binary64_14352` `count-2_binary64_14348` `associate-/l/_binary64_14347` `associate-/r/_binary64_14346` `associate-/l_binary64_14345` `associate-/r_binary64_14344` `associate-l/_binary64_14343` `associate-*r/_binary64_14342` `associate--r-_binary64_14339` `associate--l-_binary64_14338` `associate--l+_binary64_14337` `associate--r+_binary64_14336` `associate-+l-_binary64_14335` `associate-+r-_binary64_14334` `associate-+l+_binary64_14333` `associate-+r+_binary64_14332`

Counts

1 → 3

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	36	10
3	45	10
4	43	10

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	2	2	4

Error

0.0b

Counts

4 → 2

Compiler

Compiled 37 to 25 computations (32.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(.f64 x (.f64 (+.f64 x y) 2))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`pow1_binary64_14461` `add-exp-log_binary64_14438` `add-cbrt-cube_binary64_14436`
3×	`pow-prod-down_binary64_14471` `prod-exp_binary64_14449` `cbrt-unprod_binary64_14433` `associate-l_binary64_14341`
2×	`add-cube-cbrt_binary64_14435` `add-sqr-sqrt_binary64_14422` `-un-lft-identity_binary64_14400` `associate-l/_binary64_14343` `associate-*r/_binary64_14342`
1×	`add-log-exp_binary64_14439` `flip3-+_binary64_14403` `flip-+_binary64_14374` `associate-r_binary64_14340` `*-commutative_binary64_14331`

Counts

1 → 20

Calls

1 calls:

8.0ms

(*.f64 x (*.f64 (+.f64 x y) 2))

Compiler

Compiled 276 to 143 computations (48.2% saved)

series140.0ms (3.6%)

Error

0.0b

Counts

1 → 12

Calls

1 calls:

130.0ms

(*.f64 x (*.f64 (+.f64 x y) 2))

Compiler

Compiled 258 to 216 computations (16.3% saved)

simplify127.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

656×	`unswap-sqr_binary64_14368`
505×	`associate-l_binary64_14341`
335×	`associate-r_binary64_14340`
320×	`associate-+l+_binary64_14333`
307×	`distribute-rgt-in_binary64_14350`
305×	`distribute-lft-in_binary64_14349`
280×	`associate-+r+_binary64_14332`
108×	`sqr-pow_binary64_14372`
84×	`associate-*r/_binary64_14342`
83×	`associate-*l/_binary64_14343`
80×	`*-commutative_binary64_14331`
65×	`+-commutative_binary64_14330`
55×	`exp-prod_binary64_14452`
43×	`pow-sqr_binary64_14373`
33×	`distribute-rgt-out_binary64_14353`
30×	`log-prod_binary64_14486` `neg-sub0_binary64_14395` `unsub-neg_binary64_14394`
29×	`neg-mul-1_binary64_14396`
26×	`cube-prod_binary64_14428`
23×	`log-div_binary64_14487`
22×	`cube-div_binary64_14429`
20×	`times-frac_binary64_14406`
18×	`exp-sum_binary64_14446`
17×	`exp-sqrt_binary64_14453`
15×	`pow-plus_binary64_14463` `distribute-lft-neg-out_binary64_14359` `associate-/r*_binary64_14344`
14×	`distribute-rgt-neg-out_binary64_14360`
13×	`sub-neg_binary64_14393` `swap-sqr_binary64_14367` `associate-/l/_binary64_14347` `associate-/l*_binary64_14345`
12×	`unpow3_binary64_14466` `associate-/r/_binary64_14346`
10×	`exp-lft-sqr_binary64_14455` `cube-unmult_binary64_14437`
9×	`difference-of-squares_binary64_14369`
8×	`cube-mult_binary64_14430` `/-rgt-identity_binary64_14391`
6×	`prod-exp_binary64_14449`
4×	`log-pow_binary64_14489` `cancel-sign-sub-inv_binary64_14366` `associate-+r-_binary64_14334`
3×	`unpow1_binary64_14458` `distribute-rgt-neg-in_binary64_14358` `distribute-lft-out_binary64_14351` `count-2_binary64_14348`
2×	`log-rec_binary64_14488` `sub0-neg_binary64_14387` `+-rgt-identity_binary64_14385` `distribute-lft-neg-in_binary64_14357` `associate-+l-_binary64_14335`
1×	`unpow2_binary64_14465` `div-exp_binary64_14451` `rec-exp_binary64_14450` `1-exp_binary64_14444` `exp-1-e_binary64_14443` `rem-log-exp_binary64_14441` `rem-sqrt-square_binary64_14413` `-rgt-identity_binary64_14390` `-lft-identity_binary64_14389` `*-inverses_binary64_14380` `rgt-mult-inverse_binary64_14377` `distribute-rgt1-in_binary64_14356`
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_14663` `erf-erfc_binary64_14662` `erf-odd_binary64_14661` `if-if-and-not_binary64_14660` `if-if-and_binary64_14659` `if-if-or-not_binary64_14658` `if-if-or_binary64_14657` `if-not_binary64_14656` `if-same_binary64_14655` `if-false_binary64_14654` `if-true_binary64_14653` `not-gte_binary64_14652` `not-lte_binary64_14651` `not-gt_binary64_14650` `not-lt_binary64_14649` `gte-same_binary64_14648` `lte-same_binary64_14647` `gt-same_binary64_14646` `lt-same_binary64_14645` `sinh---cosh_binary64_14592` `sinh-+-cosh_binary64_14591` `sinh-cosh_binary64_14590` `tanh-def-c_binary64_14589` `tanh-def-b_binary64_14588` `tanh-def-a_binary64_14587` `cosh-def_binary64_14586` `sinh-def_binary64_14585` `tan-neg_binary64_14532` `cos-neg_binary64_14531` `sin-neg_binary64_14530` `tan-0_binary64_14529` `cos-0_binary64_14528` `sin-0_binary64_14527` `hang-m-tan_binary64_14526` `hang-p-tan_binary64_14525` `hang-m0-tan_binary64_14524` `hang-p0-tan_binary64_14523` `hang-0m-tan_binary64_14522` `hang-0p-tan_binary64_14521` `tan-+PI/2_binary64_14520` `tan-+PI_binary64_14519` `tan-PI_binary64_14518` `tan-PI/3_binary64_14517` `tan-PI/4_binary64_14516` `tan-PI/6_binary64_14515` `cos-+PI/2_binary64_14514` `cos-+PI_binary64_14513` `cos-PI_binary64_14512` `cos-PI/2_binary64_14511` `cos-PI/3_binary64_14510` `cos-PI/4_binary64_14509` `cos-PI/6_binary64_14508` `sin-+PI/2_binary64_14507` `sin-+PI_binary64_14506` `sin-PI_binary64_14505` `sin-PI/2_binary64_14504` `sin-PI/3_binary64_14503` `sin-PI/4_binary64_14502` `sin-PI/6_binary64_14501` `sub-1-sin_binary64_14500` `sub-1-cos_binary64_14499` `-1-add-sin_binary64_14498` `-1-add-cos_binary64_14497` `1-sub-sin_binary64_14496` `1-sub-cos_binary64_14495` `cos-sin-sum_binary64_14494` `log-E_binary64_14490` `pow-base-0_binary64_14484` `unpow1/3_binary64_14467` `unpow1/2_binary64_14464` `exp-to-pow_binary64_14462` `pow-base-1_binary64_14460` `unpow0_binary64_14459` `unpow-1_binary64_14457` `exp-lft-cube_binary64_14456` `exp-cbrt_binary64_14454` `exp-diff_binary64_14448` `exp-neg_binary64_14447` `e-exp-1_binary64_14445` `exp-0_binary64_14442` `rem-exp-log_binary64_14440` `cube-neg_binary64_14427` `rem-3cbrt-rft_binary64_14426` `rem-3cbrt-lft_binary64_14425` `rem-cbrt-cube_binary64_14424` `rem-cube-cbrt_binary64_14423` `sqr-abs_binary64_14415` `sqr-neg_binary64_14414` `rem-square-sqrt_binary64_14412` `div-sub_binary64_14405` `mul-1-neg_binary64_14392` `remove-double-neg_binary64_14388` `--rgt-identity_binary64_14386` `+-lft-identity_binary64_14384` `mul0-rgt_binary64_14383` `mul0-lft_binary64_14382` `div0_binary64_14381` `+-inverses_binary64_14379` `lft-mult-inverse_binary64_14378` `remove-double-div_binary64_14376` `difference-of-sqr--1_binary64_14371` `difference-of-sqr-1_binary64_14370` `cancel-sign-sub_binary64_14365` `distribute-neg-frac_binary64_14364` `distribute-frac-neg_binary64_14363` `distribute-neg-out_binary64_14362` `distribute-neg-in_binary64_14361` `distribute-lft1-in_binary64_14355` `distribute-rgt-out--_binary64_14354` `distribute-lft-out--_binary64_14352` `associate--r-_binary64_14339` `associate--l-_binary64_14338` `associate--l+_binary64_14337` `associate--r+_binary64_14336`

Counts

32 → 97

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	434
1	147	344
2	496	344
3	1966	344
4	3758	344

prune82.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	2	99

Error

Counts

99 → 2

Compiler

Compiled 1364 to 650 computations (52.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 x y))
0.0b	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))

rewrite45.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`add-sqr-sqrt_binary64_14422`
4×	`pow1_binary64_14461` `add-exp-log_binary64_14438` `add-log-exp_binary64_14439` `add-cbrt-cube_binary64_14436` `add-cube-cbrt_binary64_14435` `-un-lft-identity_binary64_14400` `associate-r*_binary64_14340`
3×	`associate-l_binary64_14341`
2×	`flip3-+_binary64_14403` `associate-*r/_binary64_14342` `flip-+_binary64_14374` `distribute-lft-out_binary64_14351`
1×	`pow-prod-down_binary64_14471` `prod-exp_binary64_14449` `cbrt-unprod_binary64_14433` `unswap-sqr_binary64_14368` `distribute-rgt-in_binary64_14350` `distribute-lft-in_binary64_14349` `*-commutative_binary64_14331` `sum-log_binary64_14491` `+-commutative_binary64_14330`

Counts

2 → 35

Calls

2 calls:

8.0ms	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
4.0ms	(+.f64 (.f64 x x) (.f64 x y))

Compiler

Compiled 608 to 186 computations (69.4% saved)

series294.0ms (7.7%)

Error

Counts

2 → 24

Calls

2 calls:

170.0ms	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
111.0ms	(+.f64 (.f64 x x) (.f64 x y))

Compiler

Compiled 480 to 393 computations (18.1% saved)

simplify183.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

336×	`associate-/l*_binary64_14345`
256×	`distribute-rgt-in_binary64_14350`
237×	`distribute-lft-in_binary64_14349`
216×	`associate-/r*_binary64_14344`
213×	`associate-+l+_binary64_14333`
204×	`associate-+r+_binary64_14332`
189×	`cube-div_binary64_14429`
179×	`*-commutative_binary64_14331`
151×	`associate-/r/_binary64_14346`
148×	`exp-prod_binary64_14452`
136×	`unswap-sqr_binary64_14368`
131×	`distribute-rgt-out_binary64_14353`
116×	`associate-l_binary64_14341`
111×	`log-div_binary64_14487`
108×	`associate-r_binary64_14340`
90×	`log-prod_binary64_14486`
83×	`cancel-sign-sub-inv_binary64_14366`
76×	`+-commutative_binary64_14330`
75×	`associate-/l/_binary64_14347`
72×	`sqr-pow_binary64_14372`
63×	`distribute-lft-out_binary64_14351`
60×	`distribute-rgt-neg-in_binary64_14358`
57×	`associate-*l/_binary64_14343`
49×	`distribute-lft-neg-in_binary64_14357`
47×	`swap-sqr_binary64_14367`
38×	`exp-sum_binary64_14446`
37×	`cube-prod_binary64_14428`
36×	`associate-+l-_binary64_14335`
35×	`exp-sqrt_binary64_14453` `sub-neg_binary64_14393`
33×	`-rgt-identity_binary64_14390` `-lft-identity_binary64_14389`
32×	`associate--l+_binary64_14337`
31×	`pow-sqr_binary64_14373`
28×	`times-frac_binary64_14406` `associate--l-_binary64_14338`
26×	`exp-lft-sqr_binary64_14455` `distribute-rgt-out--_binary64_14354`
25×	`associate-+r-_binary64_14334`
24×	`pow-plus_binary64_14463`
20×	`associate-*r/_binary64_14342`
19×	`unpow3_binary64_14466`
18×	`distribute-lft-neg-out_binary64_14359`
17×	`neg-mul-1_binary64_14396`
16×	`prod-exp_binary64_14449` `neg-sub0_binary64_14395`
15×	`cube-mult_binary64_14430`
14×	`unsub-neg_binary64_14394`
13×	`log-rec_binary64_14488`
12×	`exp-diff_binary64_14448` `distribute-lft-out--_binary64_14352`
8×	`distribute-neg-frac_binary64_14364` `distribute-rgt-neg-out_binary64_14360`
7×	`cube-unmult_binary64_14437`
6×	`difference-of-squares_binary64_14369`
5×	`log-pow_binary64_14489` `+-rgt-identity_binary64_14385` `distribute-neg-out_binary64_14362`
4×	`distribute-neg-in_binary64_14361` `distribute-rgt1-in_binary64_14356` `distribute-lft1-in_binary64_14355` `associate--r+_binary64_14336`
3×	`div-sub_binary64_14405` `/-rgt-identity_binary64_14391` `sub0-neg_binary64_14387` `count-2_binary64_14348`
2×	`unpow2_binary64_14465` `unpow1_binary64_14458`
1×	`pow-base-1_binary64_14460` `div-exp_binary64_14451` `rec-exp_binary64_14450` `1-exp_binary64_14444` `exp-1-e_binary64_14443` `rem-log-exp_binary64_14441` `rem-exp-log_binary64_14440` `rem-sqrt-square_binary64_14413` `*-inverses_binary64_14380`
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_14663` `erf-erfc_binary64_14662` `erf-odd_binary64_14661` `if-if-and-not_binary64_14660` `if-if-and_binary64_14659` `if-if-or-not_binary64_14658` `if-if-or_binary64_14657` `if-not_binary64_14656` `if-same_binary64_14655` `if-false_binary64_14654` `if-true_binary64_14653` `not-gte_binary64_14652` `not-lte_binary64_14651` `not-gt_binary64_14650` `not-lt_binary64_14649` `gte-same_binary64_14648` `lte-same_binary64_14647` `gt-same_binary64_14646` `lt-same_binary64_14645` `sinh---cosh_binary64_14592` `sinh-+-cosh_binary64_14591` `sinh-cosh_binary64_14590` `tanh-def-c_binary64_14589` `tanh-def-b_binary64_14588` `tanh-def-a_binary64_14587` `cosh-def_binary64_14586` `sinh-def_binary64_14585` `tan-neg_binary64_14532` `cos-neg_binary64_14531` `sin-neg_binary64_14530` `tan-0_binary64_14529` `cos-0_binary64_14528` `sin-0_binary64_14527` `hang-m-tan_binary64_14526` `hang-p-tan_binary64_14525` `hang-m0-tan_binary64_14524` `hang-p0-tan_binary64_14523` `hang-0m-tan_binary64_14522` `hang-0p-tan_binary64_14521` `tan-+PI/2_binary64_14520` `tan-+PI_binary64_14519` `tan-PI_binary64_14518` `tan-PI/3_binary64_14517` `tan-PI/4_binary64_14516` `tan-PI/6_binary64_14515` `cos-+PI/2_binary64_14514` `cos-+PI_binary64_14513` `cos-PI_binary64_14512` `cos-PI/2_binary64_14511` `cos-PI/3_binary64_14510` `cos-PI/4_binary64_14509` `cos-PI/6_binary64_14508` `sin-+PI/2_binary64_14507` `sin-+PI_binary64_14506` `sin-PI_binary64_14505` `sin-PI/2_binary64_14504` `sin-PI/3_binary64_14503` `sin-PI/4_binary64_14502` `sin-PI/6_binary64_14501` `sub-1-sin_binary64_14500` `sub-1-cos_binary64_14499` `-1-add-sin_binary64_14498` `-1-add-cos_binary64_14497` `1-sub-sin_binary64_14496` `1-sub-cos_binary64_14495` `cos-sin-sum_binary64_14494` `log-E_binary64_14490` `pow-base-0_binary64_14484` `unpow1/3_binary64_14467` `unpow1/2_binary64_14464` `exp-to-pow_binary64_14462` `unpow0_binary64_14459` `unpow-1_binary64_14457` `exp-lft-cube_binary64_14456` `exp-cbrt_binary64_14454` `exp-neg_binary64_14447` `e-exp-1_binary64_14445` `exp-0_binary64_14442` `cube-neg_binary64_14427` `rem-3cbrt-rft_binary64_14426` `rem-3cbrt-lft_binary64_14425` `rem-cbrt-cube_binary64_14424` `rem-cube-cbrt_binary64_14423` `sqr-abs_binary64_14415` `sqr-neg_binary64_14414` `rem-square-sqrt_binary64_14412` `mul-1-neg_binary64_14392` `remove-double-neg_binary64_14388` `--rgt-identity_binary64_14386` `+-lft-identity_binary64_14384` `mul0-rgt_binary64_14383` `mul0-lft_binary64_14382` `div0_binary64_14381` `+-inverses_binary64_14379` `lft-mult-inverse_binary64_14378` `rgt-mult-inverse_binary64_14377` `remove-double-div_binary64_14376` `difference-of-sqr--1_binary64_14371` `difference-of-sqr-1_binary64_14370` `cancel-sign-sub_binary64_14365` `distribute-frac-neg_binary64_14363` `associate--r-_binary64_14339`

Counts

59 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	682
1	191	619
2	770	616
3	1945	616
4	4525	616

prune72.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	95	2	97

Error

Counts

97 → 2

Compiler

Compiled 1391 to 553 computations (60.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (.f64 (+.f64 x y) 2))
0.3b	(.f64 (sqrt.f64 (.f64 x (.f64 (+.f64 x y) 2))) (sqrt.f64 (.f64 x (*.f64 2 (+.f64 x y)))))
7.8b	(sqrt.f64 (.f64 x (.f64 2 (+.f64 x y))))
7.8b	(sqrt.f64 (.f64 x (.f64 (+.f64 x y) 2)))

rewrite158.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

59×	`pow1_binary64_14461`
38×	`pow-prod-down_binary64_14471`
28×	`associate-*r/_binary64_14342`
24×	`sqrt-pow1_binary64_14418`
16×	`sqrt-div_binary64_14417`
12×	`associate-*l/_binary64_14343`
11×	`add-exp-log_binary64_14438` `add-cbrt-cube_binary64_14436`
9×	`add-sqr-sqrt_binary64_14422` `flip3-+_binary64_14403` `flip-+_binary64_14374`
7×	`add-cube-cbrt_binary64_14435` `-un-lft-identity_binary64_14400` `associate-l*_binary64_14341`
5×	`associate-r_binary64_14340`
4×	`pow1/2_binary64_14480` `add-log-exp_binary64_14439` `sqrt-prod_binary64_14416` `prod-exp_binary64_14449` `cbrt-unprod_binary64_14433` `frac-times_binary64_14410`
2×	`*-commutative_binary64_14331`
1×	`sqrt-unprod_binary64_14420` `unswap-sqr_binary64_14368`

Counts

4 → 87

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (.f64 x (.f64 (+.f64 x y) 2))) (sqrt.f64 (.f64 x (*.f64 2 (+.f64 x y)))))
8.0ms	(.f64 x (.f64 (+.f64 x y) 2))
6.0ms	(sqrt.f64 (.f64 x (.f64 (+.f64 x y) 2)))
6.0ms	(sqrt.f64 (.f64 x (.f64 2 (+.f64 x y))))

Compiler

Compiled 2218 to 1187 computations (46.5% saved)

series784.0ms (20.5%)

Error

Counts

4 → 48

Calls

4 calls:

316.0ms	(.f64 (sqrt.f64 (.f64 x (.f64 (+.f64 x y) 2))) (sqrt.f64 (.f64 x (*.f64 2 (+.f64 x y)))))
147.0ms	(.f64 x (.f64 (+.f64 x y) 2))
137.0ms	(sqrt.f64 (.f64 x (.f64 2 (+.f64 x y))))
133.0ms	(sqrt.f64 (.f64 x (.f64 (+.f64 x y) 2)))

Compiler

Compiled 2417 to 1922 computations (20.5% saved)

simplify461.0ms (12%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64_14406`
455×	`unswap-sqr_binary64_14368`
385×	`distribute-rgt-in_binary64_14350`
377×	`distribute-lft-in_binary64_14349`
297×	`*-commutative_binary64_14331`
161×	`associate-l_binary64_14341`
154×	`associate-r_binary64_14340`
135×	`cancel-sign-sub-inv_binary64_14366`
83×	`sqr-pow_binary64_14372`
62×	`sub-neg_binary64_14393`
56×	`exp-prod_binary64_14452` `associate-/r*_binary64_14344`
55×	`associate-/l*_binary64_14345`
44×	`swap-sqr_binary64_14367`
42×	`pow-sqr_binary64_14373` `associate-*r/_binary64_14342`
36×	`associate-*l/_binary64_14343`
32×	`log-prod_binary64_14486`
28×	`associate-+l+_binary64_14333` `+-commutative_binary64_14330`
26×	`cube-prod_binary64_14428`
25×	`neg-sub0_binary64_14395`
24×	`neg-mul-1_binary64_14396` `associate-+r+_binary64_14332`
20×	`pow-plus_binary64_14463`
15×	`associate-+r-_binary64_14334`
14×	`unsub-neg_binary64_14394` `*-rgt-identity_binary64_14390` `distribute-rgt-neg-in_binary64_14358` `associate-+l-_binary64_14335`
12×	`exp-sum_binary64_14446` `+-rgt-identity_binary64_14385`
11×	`*-lft-identity_binary64_14389`
10×	`associate-/l/_binary64_14347` `associate-/r/_binary64_14346`
9×	`rem-sqrt-square_binary64_14413` `distribute-neg-frac_binary64_14364` `distribute-lft-neg-out_binary64_14359` `distribute-lft-neg-in_binary64_14357` `distribute-rgt-out_binary64_14353`
8×	`log-div_binary64_14487` `cube-div_binary64_14429` `rem-square-sqrt_binary64_14412` `difference-of-squares_binary64_14369`
7×	`log-pow_binary64_14489` `exp-lft-sqr_binary64_14455` `div-sub_binary64_14405` `sub0-neg_binary64_14387`
6×	`unpow3_binary64_14466` `exp-sqrt_binary64_14453` `cube-unmult_binary64_14437`
5×	`cube-mult_binary64_14430`
4×	`unpow1_binary64_14458` `prod-exp_binary64_14449` `distribute-rgt-neg-out_binary64_14360`
3×	`unpow2_binary64_14465` `associate--l+_binary64_14337` `associate--r+_binary64_14336`
2×	`/-rgt-identity_binary64_14391` `*-inverses_binary64_14380` `distribute-neg-in_binary64_14361` `distribute-rgt-out--_binary64_14354`
1×	`exp-diff_binary64_14448` `1-exp_binary64_14444` `exp-1-e_binary64_14443` `rem-log-exp_binary64_14441` `mul-1-neg_binary64_14392` `mul0-rgt_binary64_14383` `mul0-lft_binary64_14382` `div0_binary64_14381` `distribute-lft-out_binary64_14351` `count-2_binary64_14348`
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_14663` `erf-erfc_binary64_14662` `erf-odd_binary64_14661` `if-if-and-not_binary64_14660` `if-if-and_binary64_14659` `if-if-or-not_binary64_14658` `if-if-or_binary64_14657` `if-not_binary64_14656` `if-same_binary64_14655` `if-false_binary64_14654` `if-true_binary64_14653` `not-gte_binary64_14652` `not-lte_binary64_14651` `not-gt_binary64_14650` `not-lt_binary64_14649` `gte-same_binary64_14648` `lte-same_binary64_14647` `gt-same_binary64_14646` `lt-same_binary64_14645` `sinh---cosh_binary64_14592` `sinh-+-cosh_binary64_14591` `sinh-cosh_binary64_14590` `tanh-def-c_binary64_14589` `tanh-def-b_binary64_14588` `tanh-def-a_binary64_14587` `cosh-def_binary64_14586` `sinh-def_binary64_14585` `tan-neg_binary64_14532` `cos-neg_binary64_14531` `sin-neg_binary64_14530` `tan-0_binary64_14529` `cos-0_binary64_14528` `sin-0_binary64_14527` `hang-m-tan_binary64_14526` `hang-p-tan_binary64_14525` `hang-m0-tan_binary64_14524` `hang-p0-tan_binary64_14523` `hang-0m-tan_binary64_14522` `hang-0p-tan_binary64_14521` `tan-+PI/2_binary64_14520` `tan-+PI_binary64_14519` `tan-PI_binary64_14518` `tan-PI/3_binary64_14517` `tan-PI/4_binary64_14516` `tan-PI/6_binary64_14515` `cos-+PI/2_binary64_14514` `cos-+PI_binary64_14513` `cos-PI_binary64_14512` `cos-PI/2_binary64_14511` `cos-PI/3_binary64_14510` `cos-PI/4_binary64_14509` `cos-PI/6_binary64_14508` `sin-+PI/2_binary64_14507` `sin-+PI_binary64_14506` `sin-PI_binary64_14505` `sin-PI/2_binary64_14504` `sin-PI/3_binary64_14503` `sin-PI/4_binary64_14502` `sin-PI/6_binary64_14501` `sub-1-sin_binary64_14500` `sub-1-cos_binary64_14499` `-1-add-sin_binary64_14498` `-1-add-cos_binary64_14497` `1-sub-sin_binary64_14496` `1-sub-cos_binary64_14495` `cos-sin-sum_binary64_14494` `log-E_binary64_14490` `log-rec_binary64_14488` `pow-base-0_binary64_14484` `unpow1/3_binary64_14467` `unpow1/2_binary64_14464` `exp-to-pow_binary64_14462` `pow-base-1_binary64_14460` `unpow0_binary64_14459` `unpow-1_binary64_14457` `exp-lft-cube_binary64_14456` `exp-cbrt_binary64_14454` `div-exp_binary64_14451` `rec-exp_binary64_14450` `exp-neg_binary64_14447` `e-exp-1_binary64_14445` `exp-0_binary64_14442` `rem-exp-log_binary64_14440` `cube-neg_binary64_14427` `rem-3cbrt-rft_binary64_14426` `rem-3cbrt-lft_binary64_14425` `rem-cbrt-cube_binary64_14424` `rem-cube-cbrt_binary64_14423` `sqr-abs_binary64_14415` `sqr-neg_binary64_14414` `remove-double-neg_binary64_14388` `--rgt-identity_binary64_14386` `+-lft-identity_binary64_14384` `+-inverses_binary64_14379` `lft-mult-inverse_binary64_14378` `rgt-mult-inverse_binary64_14377` `remove-double-div_binary64_14376` `difference-of-sqr--1_binary64_14371` `difference-of-sqr-1_binary64_14370` `cancel-sign-sub_binary64_14365` `distribute-frac-neg_binary64_14363` `distribute-neg-out_binary64_14362` `distribute-rgt1-in_binary64_14356` `distribute-lft1-in_binary64_14355` `distribute-lft-out--_binary64_14352` `associate--r-_binary64_14339` `associate--l-_binary64_14338`

Counts

135 → 340

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	2680
1	321	2097
2	1069	2031
3	2928	2031

prune477.0ms (12.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	340	2	342

Error

Counts

342 → 2

Compiler

Compiled 8124 to 4314 computations (46.9% saved)

regimes96.0ms (2.5%)

Accuracy

Total 0.0b remaining (76.6%)

Threshold costs 0.0b (76.6%)

Compiler

Compiled 660 to 508 computations (23% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64_14331`
1×	`+-commutative_binary64_14330`
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_14660` `if-if-and_binary64_14659` `if-if-or-not_binary64_14658` `if-if-or_binary64_14657` `if-not_binary64_14656` `if-same_binary64_14655` `if-false_binary64_14654` `if-true_binary64_14653` `tan-0_binary64_14529` `cos-0_binary64_14528` `sin-0_binary64_14527` `unpow1_binary64_14458` `e-exp-1_binary64_14445` `1-exp_binary64_14444` `exp-1-e_binary64_14443` `exp-0_binary64_14442` `sqr-abs_binary64_14415` `sqr-neg_binary64_14414` `neg-mul-1_binary64_14396` `neg-sub0_binary64_14395` `unsub-neg_binary64_14394` `sub-neg_binary64_14393` `mul-1-neg_binary64_14392` `/-rgt-identity_binary64_14391` `-rgt-identity_binary64_14390` `-lft-identity_binary64_14389` `remove-double-neg_binary64_14388` `sub0-neg_binary64_14387` `--rgt-identity_binary64_14386` `+-rgt-identity_binary64_14385` `+-lft-identity_binary64_14384` `cancel-sign-sub-inv_binary64_14366` `cancel-sign-sub_binary64_14365` `distribute-neg-frac_binary64_14364` `distribute-frac-neg_binary64_14363` `distribute-neg-out_binary64_14362` `distribute-neg-in_binary64_14361` `distribute-rgt-neg-out_binary64_14360` `distribute-lft-neg-out_binary64_14359` `distribute-rgt-neg-in_binary64_14358` `distribute-lft-neg-in_binary64_14357`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10

Proof

(* f64 h0 (* f64 (+ f64 h0 h1) 2))

end0.0ms (0%)

sample623.0ms (16.3%)

Algorithm

1×

intervals

Results

204.0ms	8000×	body	128	valid
3.0ms	144×	body	128	invalid

Compiler

Compiled 180 to 141 computations (21.7% saved)

Details

analyze60.0ms (1.6%)

sample18.0ms (0.5%)

simplify148.0ms (3.9%)

prune6.0ms (0.1%)

localize4.0ms (0.1%)

rewrite28.0ms (0.7%)

series140.0ms (3.6%)

simplify127.0ms (3.3%)

prune82.0ms (2.2%)

localize6.0ms (0.2%)

rewrite45.0ms (1.2%)

series294.0ms (7.7%)

simplify183.0ms (4.8%)

prune72.0ms (1.9%)

localize12.0ms (0.3%)

rewrite158.0ms (4.1%)

series784.0ms (20.5%)

simplify461.0ms (12%)

prune477.0ms (12.5%)

regimes96.0ms (2.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample623.0ms (16.3%)

Profiling