Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
75%	25%	0%	3
87.5%	12.5%	0%	4
93.7%	6.2%	0%	5
96.8%	3.1%	0%	6
98.4%	1.6%	0%	7
99.2%	0.8%	0%	8
99.6%	0.4%	0%	9
99.8%	0.2%	0%	10
99.9%	0.1%	0%	11
99.9%	0%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 6 to 6 computations (0% saved)

sample13.0ms (0.1%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

128

valid

Compiler

Compiled 11 to 12 computations (-9.1% saved)

simplify505.0ms (5%)

Algorithm

1×	egg-herbie

Rules

503×	`exp-prod_binary64_8314`
407×	`swap-sqr_binary64_8229`
380×	`associate-/l/_binary64_8209`
316×	`associate--r+_binary64_8198`
310×	`associate--l+_binary64_8199`
257×	`associate--l-_binary64_8200`
245×	`*-commutative_binary64_8193`
240×	`associate--r-_binary64_8201`
227×	`distribute-rgt1-in_binary64_8218`
225×	`unsub-neg_binary64_8256`
173×	`distribute-rgt-neg-in_binary64_8220` `associate-/r/_binary64_8208`
167×	`distribute-lft-neg-in_binary64_8219`
120×	`distribute-neg-in_binary64_8223`
104×	`sub-neg_binary64_8255`
101×	`exp-sum_binary64_8308`
83×	`distribute-rgt-in_binary64_8212`
76×	`exp-diff_binary64_8310`
75×	`neg-mul-1_binary64_8258`
73×	`neg-sub0_binary64_8257`
69×	`sqr-pow_binary64_8234`
59×	`distribute-neg-out_binary64_8224`
58×	`distribute-rgt-neg-out_binary64_8222`
55×	`distribute-lft-neg-out_binary64_8221`
52×	`pow-sqr_binary64_8235` `distribute-rgt-out_binary64_8215`
51×	`distribute-frac-neg_binary64_8225`
49×	`associate-r_binary64_8202`
48×	`pow-plus_binary64_8325`
41×	`distribute-neg-frac_binary64_8226`
39×	`associate-+l-_binary64_8197`
38×	`distribute-rgt-out--_binary64_8216`
33×	`cancel-sign-sub-inv_binary64_8228` `associate-+l+_binary64_8195`
26×	`distribute-lft-in_binary64_8211` `associate-+r+_binary64_8194`
24×	`associate-+r-_binary64_8196`
23×	`sub0-neg_binary64_8249`
22×	`associate-/l*_binary64_8207`
20×	`associate-l_binary64_8203`
19×	`+-commutative_binary64_8192`
18×	`distribute-lft1-in_binary64_8217`
14×	`sqr-neg_binary64_8276` `div-sub_binary64_8267`
11×	`exp-neg_binary64_8309` `remove-double-neg_binary64_8250`
10×	`associate-/r*_binary64_8206`
9×	`exp-lft-sqr_binary64_8317` `exp-cbrt_binary64_8316` `times-frac_binary64_8268` `count-2_binary64_8210`
8×	`cube-unmult_binary64_8299`
7×	`-rgt-identity_binary64_8252` `-lft-identity_binary64_8251` `difference-of-squares_binary64_8231` `distribute-lft-out--_binary64_8214` `distribute-lft-out_binary64_8213` `associate-*l/_binary64_8205`
6×	`+-inverses_binary64_8241`
5×	`pow-base-1_binary64_8322` `/-rgt-identity_binary64_8253` `mul0-lft_binary64_8244`
4×	`cube-prod_binary64_8290` `--rgt-identity_binary64_8248` `mul0-rgt_binary64_8245` `unswap-sqr_binary64_8230` `associate-*r/_binary64_8204`
3×	`+-rgt-identity_binary64_8247` `div0_binary64_8243`
2×	`difference-of-sqr-1_binary64_8232`
1×	`exp-sqrt_binary64_8315` `prod-exp_binary64_8311` `1-exp_binary64_8306` `exp-1-e_binary64_8305` `cube-div_binary64_8291` `cube-neg_binary64_8289` `+-lft-identity_binary64_8246` `*-inverses_binary64_8242` `difference-of-sqr--1_binary64_8233` `cancel-sign-sub_binary64_8227`
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_8525` `erf-erfc_binary64_8524` `erf-odd_binary64_8523` `if-if-and-not_binary64_8522` `if-if-and_binary64_8521` `if-if-or-not_binary64_8520` `if-if-or_binary64_8519` `if-not_binary64_8518` `if-same_binary64_8517` `if-false_binary64_8516` `if-true_binary64_8515` `not-gte_binary64_8514` `not-lte_binary64_8513` `not-gt_binary64_8512` `not-lt_binary64_8511` `gte-same_binary64_8510` `lte-same_binary64_8509` `gt-same_binary64_8508` `lt-same_binary64_8507` `sinh---cosh_binary64_8454` `sinh-+-cosh_binary64_8453` `sinh-cosh_binary64_8452` `tanh-def-c_binary64_8451` `tanh-def-b_binary64_8450` `tanh-def-a_binary64_8449` `cosh-def_binary64_8448` `sinh-def_binary64_8447` `tan-neg_binary64_8394` `cos-neg_binary64_8393` `sin-neg_binary64_8392` `tan-0_binary64_8391` `cos-0_binary64_8390` `sin-0_binary64_8389` `hang-m-tan_binary64_8388` `hang-p-tan_binary64_8387` `hang-m0-tan_binary64_8386` `hang-p0-tan_binary64_8385` `hang-0m-tan_binary64_8384` `hang-0p-tan_binary64_8383` `tan-+PI/2_binary64_8382` `tan-+PI_binary64_8381` `tan-PI_binary64_8380` `tan-PI/3_binary64_8379` `tan-PI/4_binary64_8378` `tan-PI/6_binary64_8377` `cos-+PI/2_binary64_8376` `cos-+PI_binary64_8375` `cos-PI_binary64_8374` `cos-PI/2_binary64_8373` `cos-PI/3_binary64_8372` `cos-PI/4_binary64_8371` `cos-PI/6_binary64_8370` `sin-+PI/2_binary64_8369` `sin-+PI_binary64_8368` `sin-PI_binary64_8367` `sin-PI/2_binary64_8366` `sin-PI/3_binary64_8365` `sin-PI/4_binary64_8364` `sin-PI/6_binary64_8363` `sub-1-sin_binary64_8362` `sub-1-cos_binary64_8361` `-1-add-sin_binary64_8360` `-1-add-cos_binary64_8359` `1-sub-sin_binary64_8358` `1-sub-cos_binary64_8357` `cos-sin-sum_binary64_8356` `log-E_binary64_8352` `log-pow_binary64_8351` `log-rec_binary64_8350` `log-div_binary64_8349` `log-prod_binary64_8348` `pow-base-0_binary64_8346` `unpow1/3_binary64_8329` `unpow3_binary64_8328` `unpow2_binary64_8327` `unpow1/2_binary64_8326` `exp-to-pow_binary64_8324` `unpow0_binary64_8321` `unpow1_binary64_8320` `unpow-1_binary64_8319` `exp-lft-cube_binary64_8318` `div-exp_binary64_8313` `rec-exp_binary64_8312` `e-exp-1_binary64_8307` `exp-0_binary64_8304` `rem-log-exp_binary64_8303` `rem-exp-log_binary64_8302` `cube-mult_binary64_8292` `rem-3cbrt-rft_binary64_8288` `rem-3cbrt-lft_binary64_8287` `rem-cbrt-cube_binary64_8286` `rem-cube-cbrt_binary64_8285` `sqr-abs_binary64_8277` `rem-sqrt-square_binary64_8275` `rem-square-sqrt_binary64_8274` `mul-1-neg_binary64_8254` `lft-mult-inverse_binary64_8240` `rgt-mult-inverse_binary64_8239` `remove-double-div_binary64_8238`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	10	7
2	16	7
3	24	7
4	38	7
5	74	7
6	132	7
7	512	7
8	1617	7

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 10 to 10 computations (0% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 x (/.f64 1 3))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`add-sqr-sqrt_binary64_8284`
13×	`cancel-sign-sub-inv_binary64_8228`
12×	`*-un-lft-identity_binary64_8262`
11×	`times-frac_binary64_8268`
8×	`add-cube-cbrt_binary64_8297`
3×	`add-log-exp_binary64_8301` `difference-of-squares_binary64_8231`
2×	`div-inv_binary64_8259` `distribute-lft-out--_binary64_8214`
1×	`diff-log_binary64_8354` `pow1_binary64_8323` `add-exp-log_binary64_8300` `add-cbrt-cube_binary64_8298` `flip3--_binary64_8266` `sub-neg_binary64_8255` `flip--_binary64_8237`

Counts

1 → 29

Calls

1 calls:

10.0ms

(-.f64 x (/.f64 1 3))

Compiler

Compiled 375 to 328 computations (12.5% saved)

series37.0ms (0.4%)

Error

0.0b

Counts

1 → 6

Calls

1 calls:

32.0ms

(-.f64 x (/.f64 1 3))

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify1.6s (15.5%)

Algorithm

1×	egg-herbie

Rules

655×	`unsub-neg_binary64_8256`
527×	`associate-/l/_binary64_8209`
272×	`distribute-rgt-in_binary64_8212`
269×	`distribute-frac-neg_binary64_8225`
256×	`associate-/r*_binary64_8206`
233×	`distribute-lft-in_binary64_8211`
231×	`associate-/r/_binary64_8208`
202×	`difference-of-squares_binary64_8231`
196×	`distribute-neg-out_binary64_8224`
185×	`exp-prod_binary64_8314`
162×	`div-sub_binary64_8267`
153×	`sub-neg_binary64_8255`
137×	`sqr-pow_binary64_8234` `associate-l_binary64_8203`
135×	`neg-sub0_binary64_8257` `associate-/l*_binary64_8207`
134×	`neg-mul-1_binary64_8258`
120×	`associate-r_binary64_8202` `*-commutative_binary64_8193`
90×	`distribute-lft-neg-out_binary64_8221`
85×	`distribute-neg-frac_binary64_8226` `associate-*l/_binary64_8205`
76×	`distribute-rgt-neg-out_binary64_8222`
71×	`cube-div_binary64_8291`
69×	`pow-sqr_binary64_8235`
64×	`cube-prod_binary64_8290`
62×	`times-frac_binary64_8268` `associate-*r/_binary64_8204`
59×	`unswap-sqr_binary64_8230`
58×	`*-lft-identity_binary64_8251`
54×	`exp-sum_binary64_8308`
53×	`cancel-sign-sub-inv_binary64_8228`
52×	`swap-sqr_binary64_8229`
51×	`exp-diff_binary64_8310`
46×	`sub0-neg_binary64_8249`
44×	`*-rgt-identity_binary64_8252`
43×	`mul0-rgt_binary64_8245` `mul0-lft_binary64_8244`
39×	`associate-+l-_binary64_8197`
38×	`associate-+r+_binary64_8194`
33×	`distribute-lft-out_binary64_8213` `+-commutative_binary64_8192`
30×	`associate-+l+_binary64_8195`
28×	`sqr-neg_binary64_8276`
26×	`pow-plus_binary64_8325`
24×	`distribute-rgt-neg-in_binary64_8220` `associate--l-_binary64_8200`
22×	`remove-double-div_binary64_8238`
20×	`+-lft-identity_binary64_8246`
18×	`div0_binary64_8243`
17×	`/-rgt-identity_binary64_8253`
16×	`log-pow_binary64_8351`
15×	`unpow3_binary64_8328` `rem-sqrt-square_binary64_8275` `distribute-rgt-out_binary64_8215`
14×	`exp-neg_binary64_8309` `distribute-lft-neg-in_binary64_8219`
13×	`cube-unmult_binary64_8299` `cube-mult_binary64_8292`
10×	`div-exp_binary64_8313` `prod-exp_binary64_8311` `--rgt-identity_binary64_8248` `associate--r+_binary64_8198`
8×	`+-rgt-identity_binary64_8247` `associate-+r-_binary64_8196`
7×	`log-prod_binary64_8348` `distribute-rgt-out--_binary64_8216`
6×	`pow-base-1_binary64_8322` `mul-1-neg_binary64_8254`
4×	`exp-cbrt_binary64_8316`
3×	`rec-exp_binary64_8312` `rem-square-sqrt_binary64_8274` `remove-double-neg_binary64_8250`
2×	`log-div_binary64_8349` `rem-3cbrt-lft_binary64_8287` `rem-cbrt-cube_binary64_8286` `+-inverses_binary64_8241` `difference-of-sqr-1_binary64_8232` `distribute-neg-in_binary64_8223`
1×	`log-rec_binary64_8350` `1-exp_binary64_8306` `exp-1-e_binary64_8305` `rem-log-exp_binary64_8303` `cube-neg_binary64_8289` `rem-3cbrt-rft_binary64_8288` `*-inverses_binary64_8242` `distribute-rgt1-in_binary64_8218` `distribute-lft1-in_binary64_8217` `distribute-lft-out--_binary64_8214` `count-2_binary64_8210`
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_8525` `erf-erfc_binary64_8524` `erf-odd_binary64_8523` `if-if-and-not_binary64_8522` `if-if-and_binary64_8521` `if-if-or-not_binary64_8520` `if-if-or_binary64_8519` `if-not_binary64_8518` `if-same_binary64_8517` `if-false_binary64_8516` `if-true_binary64_8515` `not-gte_binary64_8514` `not-lte_binary64_8513` `not-gt_binary64_8512` `not-lt_binary64_8511` `gte-same_binary64_8510` `lte-same_binary64_8509` `gt-same_binary64_8508` `lt-same_binary64_8507` `sinh---cosh_binary64_8454` `sinh-+-cosh_binary64_8453` `sinh-cosh_binary64_8452` `tanh-def-c_binary64_8451` `tanh-def-b_binary64_8450` `tanh-def-a_binary64_8449` `cosh-def_binary64_8448` `sinh-def_binary64_8447` `tan-neg_binary64_8394` `cos-neg_binary64_8393` `sin-neg_binary64_8392` `tan-0_binary64_8391` `cos-0_binary64_8390` `sin-0_binary64_8389` `hang-m-tan_binary64_8388` `hang-p-tan_binary64_8387` `hang-m0-tan_binary64_8386` `hang-p0-tan_binary64_8385` `hang-0m-tan_binary64_8384` `hang-0p-tan_binary64_8383` `tan-+PI/2_binary64_8382` `tan-+PI_binary64_8381` `tan-PI_binary64_8380` `tan-PI/3_binary64_8379` `tan-PI/4_binary64_8378` `tan-PI/6_binary64_8377` `cos-+PI/2_binary64_8376` `cos-+PI_binary64_8375` `cos-PI_binary64_8374` `cos-PI/2_binary64_8373` `cos-PI/3_binary64_8372` `cos-PI/4_binary64_8371` `cos-PI/6_binary64_8370` `sin-+PI/2_binary64_8369` `sin-+PI_binary64_8368` `sin-PI_binary64_8367` `sin-PI/2_binary64_8366` `sin-PI/3_binary64_8365` `sin-PI/4_binary64_8364` `sin-PI/6_binary64_8363` `sub-1-sin_binary64_8362` `sub-1-cos_binary64_8361` `-1-add-sin_binary64_8360` `-1-add-cos_binary64_8359` `1-sub-sin_binary64_8358` `1-sub-cos_binary64_8357` `cos-sin-sum_binary64_8356` `log-E_binary64_8352` `pow-base-0_binary64_8346` `unpow1/3_binary64_8329` `unpow2_binary64_8327` `unpow1/2_binary64_8326` `exp-to-pow_binary64_8324` `unpow0_binary64_8321` `unpow1_binary64_8320` `unpow-1_binary64_8319` `exp-lft-cube_binary64_8318` `exp-lft-sqr_binary64_8317` `exp-sqrt_binary64_8315` `e-exp-1_binary64_8307` `exp-0_binary64_8304` `rem-exp-log_binary64_8302` `rem-cube-cbrt_binary64_8285` `sqr-abs_binary64_8277` `lft-mult-inverse_binary64_8240` `rgt-mult-inverse_binary64_8239` `difference-of-sqr--1_binary64_8233` `cancel-sign-sub_binary64_8227` `associate--r-_binary64_8201` `associate--l+_binary64_8199`

Counts

35 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	337
1	229	291
2	618	288
3	1287	288
4	3360	288

prune43.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	2	51

Error

0.0b

Counts

51 → 2

Compiler

Compiled 531 to 431 computations (18.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3)))
0.0b	(+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (.f64 x (/.f64 1 3)))
0.3b	(*.f64 x (/.f64 1 3))
21.3b	(/.f64 (+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3))) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 x (/.f64 1 3)))))

rewrite376.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`*-un-lft-identity_binary64_8262`
28×	`add-sqr-sqrt_binary64_8284`
23×	`times-frac_binary64_8268`
21×	`add-cube-cbrt_binary64_8297`
15×	`add-exp-log_binary64_8300`
13×	`associate-r_binary64_8202`
11×	`add-cbrt-cube_binary64_8298`
8×	`add-log-exp_binary64_8301` `frac-add_binary64_8270`
7×	`un-div-inv_binary64_8260` `associate-*r/_binary64_8204`
6×	`pow1_binary64_8323`
5×	`distribute-lft-out_binary64_8213`
4×	`flip3-+_binary64_8265` `flip-+_binary64_8236` `associate-/l*_binary64_8207` `prod-exp_binary64_8311`
3×	`div-exp_binary64_8313` `associate-/r_binary64_8206` `unswap-sqr_binary64_8230` `associate-l*_binary64_8203`
2×	`cbrt-undiv_binary64_8296` `div-inv_binary64_8259` `associate-/l/_binary64_8209` `associate-/r/_binary64_8208` `cbrt-unprod_binary64_8295` `sum-log_binary64_8353` `frac-times_binary64_8272` `associate-*l/_binary64_8205` `+-commutative_binary64_8192`
1×	`frac-2neg_binary64_8273` `clear-num_binary64_8261` `pow-prod-down_binary64_8333` `1-exp_binary64_8306` `rec-exp_binary64_8312` `*-commutative_binary64_8193` `distribute-rgt-out_binary64_8215`

Counts

4 → 103

Calls

4 calls:

46.0ms	(/.f64 (+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3))) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 x (/.f64 1 3)))))
29.0ms	(+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3)))
12.0ms	(+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (.f64 x (/.f64 1 3)))
8.0ms	(*.f64 x (/.f64 1 3))

Compiler

Compiled 4140 to 3444 computations (16.8% saved)

series320.0ms (3.2%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

140.0ms	(/.f64 (+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3))) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 x (/.f64 1 3)))))
82.0ms	(+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3)))
47.0ms	(+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (.f64 x (/.f64 1 3)))
26.0ms	(*.f64 x (/.f64 1 3))

Compiler

Compiled 856 to 711 computations (16.9% saved)

simplify597.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

455×	`distribute-rgt-in_binary64_8212`
448×	`associate-/r/_binary64_8208`
416×	`distribute-lft-in_binary64_8211`
197×	`cancel-sign-sub-inv_binary64_8228`
137×	`associate-l_binary64_8203`
124×	`associate-r_binary64_8202`
116×	`distribute-rgt-neg-in_binary64_8220`
103×	`times-frac_binary64_8268`
101×	`distribute-rgt-out_binary64_8215`
100×	`distribute-lft-neg-in_binary64_8219`
92×	`associate-/l*_binary64_8207`
83×	`associate-+l+_binary64_8195`
79×	`unswap-sqr_binary64_8230`
75×	`associate-+r+_binary64_8194`
74×	`associate-*l/_binary64_8205`
72×	`associate-*r/_binary64_8204`
63×	`sqr-pow_binary64_8234` `*-commutative_binary64_8193`
62×	`cube-prod_binary64_8290`
58×	`distribute-neg-frac_binary64_8226`
56×	`associate-/l/_binary64_8209`
53×	`sub-neg_binary64_8255`
52×	`associate-/r*_binary64_8206`
44×	`distribute-rgt-out--_binary64_8216`
43×	`exp-prod_binary64_8314` `associate--l+_binary64_8199`
41×	`cube-div_binary64_8291`
40×	`associate--l-_binary64_8200`
38×	`swap-sqr_binary64_8229` `distribute-lft-out_binary64_8213`
35×	`log-prod_binary64_8348`
34×	`associate-+l-_binary64_8197`
31×	`neg-mul-1_binary64_8258`
30×	`neg-sub0_binary64_8257` `pow-sqr_binary64_8235`
28×	`associate-+r-_binary64_8196`
26×	`+-commutative_binary64_8192`
25×	`associate--r+_binary64_8198`
24×	`log-div_binary64_8349`
23×	`*-rgt-identity_binary64_8252` `distribute-neg-in_binary64_8223`
19×	`distribute-lft-neg-out_binary64_8221`
18×	`div-sub_binary64_8267`
17×	`/-rgt-identity_binary64_8253`
15×	`unpow3_binary64_8328`
13×	`cube-mult_binary64_8292`
12×	`*-lft-identity_binary64_8251`
11×	`pow-plus_binary64_8325` `exp-cbrt_binary64_8316`
10×	`distribute-frac-neg_binary64_8225` `distribute-lft-out--_binary64_8214`
7×	`difference-of-squares_binary64_8231`
6×	`exp-lft-cube_binary64_8318` `unsub-neg_binary64_8256` `distribute-rgt-neg-out_binary64_8222` `distribute-rgt1-in_binary64_8218`
5×	`cube-unmult_binary64_8299`
4×	`log-rec_binary64_8350`
3×	`prod-exp_binary64_8311` `mul-1-neg_binary64_8254`
2×	`exp-sum_binary64_8308` `remove-double-neg_binary64_8250` `distribute-neg-out_binary64_8224` `associate--r-_binary64_8201`
1×	`log-pow_binary64_8351` `div-exp_binary64_8313` `rec-exp_binary64_8312` `exp-diff_binary64_8310` `1-exp_binary64_8306` `exp-1-e_binary64_8305` `rem-log-exp_binary64_8303` `rem-cbrt-cube_binary64_8286` `rem-sqrt-square_binary64_8275` `sub0-neg_binary64_8249` `lft-mult-inverse_binary64_8240` `remove-double-div_binary64_8238` `distribute-lft1-in_binary64_8217` `count-2_binary64_8210`
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_8525` `erf-erfc_binary64_8524` `erf-odd_binary64_8523` `if-if-and-not_binary64_8522` `if-if-and_binary64_8521` `if-if-or-not_binary64_8520` `if-if-or_binary64_8519` `if-not_binary64_8518` `if-same_binary64_8517` `if-false_binary64_8516` `if-true_binary64_8515` `not-gte_binary64_8514` `not-lte_binary64_8513` `not-gt_binary64_8512` `not-lt_binary64_8511` `gte-same_binary64_8510` `lte-same_binary64_8509` `gt-same_binary64_8508` `lt-same_binary64_8507` `sinh---cosh_binary64_8454` `sinh-+-cosh_binary64_8453` `sinh-cosh_binary64_8452` `tanh-def-c_binary64_8451` `tanh-def-b_binary64_8450` `tanh-def-a_binary64_8449` `cosh-def_binary64_8448` `sinh-def_binary64_8447` `tan-neg_binary64_8394` `cos-neg_binary64_8393` `sin-neg_binary64_8392` `tan-0_binary64_8391` `cos-0_binary64_8390` `sin-0_binary64_8389` `hang-m-tan_binary64_8388` `hang-p-tan_binary64_8387` `hang-m0-tan_binary64_8386` `hang-p0-tan_binary64_8385` `hang-0m-tan_binary64_8384` `hang-0p-tan_binary64_8383` `tan-+PI/2_binary64_8382` `tan-+PI_binary64_8381` `tan-PI_binary64_8380` `tan-PI/3_binary64_8379` `tan-PI/4_binary64_8378` `tan-PI/6_binary64_8377` `cos-+PI/2_binary64_8376` `cos-+PI_binary64_8375` `cos-PI_binary64_8374` `cos-PI/2_binary64_8373` `cos-PI/3_binary64_8372` `cos-PI/4_binary64_8371` `cos-PI/6_binary64_8370` `sin-+PI/2_binary64_8369` `sin-+PI_binary64_8368` `sin-PI_binary64_8367` `sin-PI/2_binary64_8366` `sin-PI/3_binary64_8365` `sin-PI/4_binary64_8364` `sin-PI/6_binary64_8363` `sub-1-sin_binary64_8362` `sub-1-cos_binary64_8361` `-1-add-sin_binary64_8360` `-1-add-cos_binary64_8359` `1-sub-sin_binary64_8358` `1-sub-cos_binary64_8357` `cos-sin-sum_binary64_8356` `log-E_binary64_8352` `pow-base-0_binary64_8346` `unpow1/3_binary64_8329` `unpow2_binary64_8327` `unpow1/2_binary64_8326` `exp-to-pow_binary64_8324` `pow-base-1_binary64_8322` `unpow0_binary64_8321` `unpow1_binary64_8320` `unpow-1_binary64_8319` `exp-lft-sqr_binary64_8317` `exp-sqrt_binary64_8315` `exp-neg_binary64_8309` `e-exp-1_binary64_8307` `exp-0_binary64_8304` `rem-exp-log_binary64_8302` `cube-neg_binary64_8289` `rem-3cbrt-rft_binary64_8288` `rem-3cbrt-lft_binary64_8287` `rem-cube-cbrt_binary64_8285` `sqr-abs_binary64_8277` `sqr-neg_binary64_8276` `rem-square-sqrt_binary64_8274` `--rgt-identity_binary64_8248` `+-rgt-identity_binary64_8247` `+-lft-identity_binary64_8246` `mul0-rgt_binary64_8245` `mul0-lft_binary64_8244` `div0_binary64_8243` `*-inverses_binary64_8242` `+-inverses_binary64_8241` `rgt-mult-inverse_binary64_8239` `difference-of-sqr--1_binary64_8233` `difference-of-sqr-1_binary64_8232` `cancel-sign-sub_binary64_8227`

Counts

124 → 268

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2897
1	479	2520
2	1826	2470

prune1.0s (10.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	267	3	270

Error

Counts

270 → 3

Compiler

Compiled 11202 to 9093 computations (18.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.4b	(/.f64 (+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3))) (sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3))))
15.2b	(sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))
15.2b	(sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))
15.3b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))) (/.f64 (+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3))) (sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))))

rewrite982.0ms (9.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

99×	`add-sqr-sqrt_binary64_8284`
88×	`times-frac_binary64_8268`
83×	`*-un-lft-identity_binary64_8262`
53×	`sqrt-prod_binary64_8278`
51×	`add-cube-cbrt_binary64_8297`
30×	`associate-r_binary64_8202`
28×	`add-exp-log_binary64_8300`
24×	`associate-l_binary64_8203`
18×	`add-cbrt-cube_binary64_8298`
15×	`unswap-sqr_binary64_8230`
13×	`distribute-lft-out_binary64_8213`
10×	`sqrt-div_binary64_8279`
9×	`div-exp_binary64_8313`
8×	`pow1_binary64_8323` `prod-exp_binary64_8311`
6×	`flip3-+_binary64_8265` `associate-/r/_binary64_8208` `flip-+_binary64_8236` `associate-/r*_binary64_8206`
5×	`cbrt-undiv_binary64_8296`
4×	`add-log-exp_binary64_8301` `cbrt-unprod_binary64_8295` `associate-/l*_binary64_8207`
3×	`div-inv_binary64_8259`
2×	`1-exp_binary64_8306` `rec-exp_binary64_8312` `pow1/2_binary64_8342` `sqrt-pow1_binary64_8280` `rem-sqrt-square_binary64_8275` `associate-/l/_binary64_8209`
1×	`pow-prod-down_binary64_8333` `frac-times_binary64_8272` `associate-l/_binary64_8205` `associate-r/_binary64_8204` `*-commutative_binary64_8193` `frac-2neg_binary64_8273` `clear-num_binary64_8261`

Counts

4 → 173

Calls

4 calls:

80.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))) (/.f64 (+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3))) (sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))))
43.0ms	(/.f64 (+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3))) (sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3))))
18.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))
12.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))

Compiler

Compiled 10255 to 7881 computations (23.1% saved)

series397.0ms (3.9%)

Error

Counts

4 → 42

Calls

4 calls:

128.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))) (/.f64 (+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3))) (sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))))
78.0ms	(/.f64 (+.f64 (pow.f64 x 3) (/.f64 -1 (pow.f64 3 3))) (sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3))))
63.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))
61.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 x (/.f64 1 3)) 3)))

Compiler

Compiled 2193 to 1803 computations (17.8% saved)

simplify751.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

514×	`distribute-rgt-in_binary64_8212`
485×	`distribute-lft-in_binary64_8211`
342×	`associate-/r/_binary64_8208`
249×	`associate-/r*_binary64_8206`
223×	`associate-r_binary64_8202`
179×	`associate-l_binary64_8203`
173×	`associate-*l/_binary64_8205`
168×	`associate-/l*_binary64_8207`
163×	`associate-*r/_binary64_8204`
146×	`cancel-sign-sub-inv_binary64_8228`
126×	`*-commutative_binary64_8193`
91×	`sub-neg_binary64_8255`
75×	`associate-/l/_binary64_8209`
62×	`distribute-rgt-neg-in_binary64_8220`
50×	`+-commutative_binary64_8192`
47×	`times-frac_binary64_8268`
45×	`*-lft-identity_binary64_8251`
43×	`distribute-lft-neg-in_binary64_8219`
42×	`neg-mul-1_binary64_8258` `neg-sub0_binary64_8257` `distribute-neg-in_binary64_8223`
41×	`sqr-pow_binary64_8234`
37×	`distribute-rgt-out_binary64_8215`
36×	`*-rgt-identity_binary64_8252`
32×	`distribute-neg-frac_binary64_8226`
31×	`unswap-sqr_binary64_8230`
29×	`exp-prod_binary64_8314`
26×	`associate--l+_binary64_8199`
22×	`log-div_binary64_8349` `distribute-rgt-out--_binary64_8216`
21×	`unsub-neg_binary64_8256` `distribute-lft-out_binary64_8213`
20×	`/-rgt-identity_binary64_8253`
18×	`pow-sqr_binary64_8235` `associate-+l+_binary64_8195`
17×	`distribute-lft-neg-out_binary64_8221` `associate--r+_binary64_8198`
16×	`cube-div_binary64_8291`
15×	`div-sub_binary64_8267` `swap-sqr_binary64_8229`
11×	`log-prod_binary64_8348`
10×	`pow-plus_binary64_8325`
9×	`log-rec_binary64_8350` `distribute-frac-neg_binary64_8225`
8×	`distribute-neg-out_binary64_8224` `distribute-lft-out--_binary64_8214` `associate-+r+_binary64_8194`
7×	`exp-sum_binary64_8308` `cube-unmult_binary64_8299`
6×	`unpow3_binary64_8328` `cube-prod_binary64_8290` `associate-+l-_binary64_8197`
5×	`cube-mult_binary64_8292` `mul-1-neg_binary64_8254`
3×	`rem-sqrt-square_binary64_8275` `distribute-rgt-neg-out_binary64_8222` `associate-+r-_binary64_8196`
2×	`sub0-neg_binary64_8249` `count-2_binary64_8210`
1×	`log-pow_binary64_8351` `unpow2_binary64_8327` `unpow1_binary64_8320` `exp-sqrt_binary64_8315` `div-exp_binary64_8313` `rec-exp_binary64_8312` `prod-exp_binary64_8311` `1-exp_binary64_8306` `exp-1-e_binary64_8305` `rem-log-exp_binary64_8303` `rem-cbrt-cube_binary64_8286` `rem-square-sqrt_binary64_8274` `remove-double-neg_binary64_8250` `*-inverses_binary64_8242` `remove-double-div_binary64_8238` `difference-of-squares_binary64_8231` `associate--r-_binary64_8201`
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_8525` `erf-erfc_binary64_8524` `erf-odd_binary64_8523` `if-if-and-not_binary64_8522` `if-if-and_binary64_8521` `if-if-or-not_binary64_8520` `if-if-or_binary64_8519` `if-not_binary64_8518` `if-same_binary64_8517` `if-false_binary64_8516` `if-true_binary64_8515` `not-gte_binary64_8514` `not-lte_binary64_8513` `not-gt_binary64_8512` `not-lt_binary64_8511` `gte-same_binary64_8510` `lte-same_binary64_8509` `gt-same_binary64_8508` `lt-same_binary64_8507` `sinh---cosh_binary64_8454` `sinh-+-cosh_binary64_8453` `sinh-cosh_binary64_8452` `tanh-def-c_binary64_8451` `tanh-def-b_binary64_8450` `tanh-def-a_binary64_8449` `cosh-def_binary64_8448` `sinh-def_binary64_8447` `tan-neg_binary64_8394` `cos-neg_binary64_8393` `sin-neg_binary64_8392` `tan-0_binary64_8391` `cos-0_binary64_8390` `sin-0_binary64_8389` `hang-m-tan_binary64_8388` `hang-p-tan_binary64_8387` `hang-m0-tan_binary64_8386` `hang-p0-tan_binary64_8385` `hang-0m-tan_binary64_8384` `hang-0p-tan_binary64_8383` `tan-+PI/2_binary64_8382` `tan-+PI_binary64_8381` `tan-PI_binary64_8380` `tan-PI/3_binary64_8379` `tan-PI/4_binary64_8378` `tan-PI/6_binary64_8377` `cos-+PI/2_binary64_8376` `cos-+PI_binary64_8375` `cos-PI_binary64_8374` `cos-PI/2_binary64_8373` `cos-PI/3_binary64_8372` `cos-PI/4_binary64_8371` `cos-PI/6_binary64_8370` `sin-+PI/2_binary64_8369` `sin-+PI_binary64_8368` `sin-PI_binary64_8367` `sin-PI/2_binary64_8366` `sin-PI/3_binary64_8365` `sin-PI/4_binary64_8364` `sin-PI/6_binary64_8363` `sub-1-sin_binary64_8362` `sub-1-cos_binary64_8361` `-1-add-sin_binary64_8360` `-1-add-cos_binary64_8359` `1-sub-sin_binary64_8358` `1-sub-cos_binary64_8357` `cos-sin-sum_binary64_8356` `log-E_binary64_8352` `pow-base-0_binary64_8346` `unpow1/3_binary64_8329` `unpow1/2_binary64_8326` `exp-to-pow_binary64_8324` `pow-base-1_binary64_8322` `unpow0_binary64_8321` `unpow-1_binary64_8319` `exp-lft-cube_binary64_8318` `exp-lft-sqr_binary64_8317` `exp-cbrt_binary64_8316` `exp-diff_binary64_8310` `exp-neg_binary64_8309` `e-exp-1_binary64_8307` `exp-0_binary64_8304` `rem-exp-log_binary64_8302` `cube-neg_binary64_8289` `rem-3cbrt-rft_binary64_8288` `rem-3cbrt-lft_binary64_8287` `rem-cube-cbrt_binary64_8285` `sqr-abs_binary64_8277` `sqr-neg_binary64_8276` `--rgt-identity_binary64_8248` `+-rgt-identity_binary64_8247` `+-lft-identity_binary64_8246` `mul0-rgt_binary64_8245` `mul0-lft_binary64_8244` `div0_binary64_8243` `+-inverses_binary64_8241` `lft-mult-inverse_binary64_8240` `rgt-mult-inverse_binary64_8239` `difference-of-sqr--1_binary64_8233` `difference-of-sqr-1_binary64_8232` `cancel-sign-sub_binary64_8227` `distribute-rgt1-in_binary64_8218` `distribute-lft1-in_binary64_8217` `associate--l-_binary64_8200`

Counts

215 → 344

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	10580
1	679	9143
2	2601	9038

prune2.3s (23.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	344	3	347

Error

Counts

347 → 3

Compiler

Compiled 19384 to 14924 computations (23% saved)

regimes131.0ms (1.3%)

Accuracy

Total 0.0b remaining (97.4%)

Threshold costs 0.0b (97.4%)

Compiler

Compiled 1212 to 1069 computations (11.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`sub-neg_binary64_8255` `+-commutative_binary64_8192`
1×	`neg-mul-1_binary64_8258` `neg-sub0_binary64_8257` `*-commutative_binary64_8193`
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_8522` `if-if-and_binary64_8521` `if-if-or-not_binary64_8520` `if-if-or_binary64_8519` `if-not_binary64_8518` `if-same_binary64_8517` `if-false_binary64_8516` `if-true_binary64_8515` `tan-0_binary64_8391` `cos-0_binary64_8390` `sin-0_binary64_8389` `unpow1_binary64_8320` `e-exp-1_binary64_8307` `1-exp_binary64_8306` `exp-1-e_binary64_8305` `exp-0_binary64_8304` `sqr-abs_binary64_8277` `sqr-neg_binary64_8276` `unsub-neg_binary64_8256` `mul-1-neg_binary64_8254` `/-rgt-identity_binary64_8253` `-rgt-identity_binary64_8252` `-lft-identity_binary64_8251` `remove-double-neg_binary64_8250` `sub0-neg_binary64_8249` `--rgt-identity_binary64_8248` `+-rgt-identity_binary64_8247` `+-lft-identity_binary64_8246` `cancel-sign-sub-inv_binary64_8228` `cancel-sign-sub_binary64_8227` `distribute-neg-frac_binary64_8226` `distribute-frac-neg_binary64_8225` `distribute-neg-out_binary64_8224` `distribute-neg-in_binary64_8223` `distribute-rgt-neg-out_binary64_8222` `distribute-lft-neg-out_binary64_8221` `distribute-rgt-neg-in_binary64_8220` `distribute-lft-neg-in_binary64_8219`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	6	4
2	11	4
3	13	4
4	14	4

Proof

(- f64 h0 1/3)

end0.0ms (0%)

sample930.0ms (9.2%)

Algorithm

1×

intervals

Results

144.0ms

8000×

body

128

valid

Compiler

Compiled 600 to 528 computations (12% saved)

Details

analyze3.0ms (0%)

sample13.0ms (0.1%)

simplify505.0ms (5%)

prune3.0ms (0%)

localize4.0ms (0%)

rewrite44.0ms (0.4%)

series37.0ms (0.4%)

simplify1.6s (15.5%)

prune43.0ms (0.4%)

localize15.0ms (0.1%)

rewrite376.0ms (3.7%)

series320.0ms (3.2%)

simplify597.0ms (5.9%)

prune1.0s (10.1%)

localize17.0ms (0.2%)

rewrite982.0ms (9.8%)

series397.0ms (3.9%)

simplify751.0ms (7.5%)

prune2.3s (23.1%)

regimes131.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample930.0ms (9.2%)

Profiling