Details

Time bar (total: 10.0s)

analyze19.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
50%50%0.1%3
74.9%25%0.1%4
74.9%25%0.1%5
87.4%12.5%0.1%6
87.4%12.5%0.1%7
93.7%6.2%0.1%8
93.7%6.2%0.1%9
96.8%3.1%0.1%10
96.8%3.1%0.1%11
98.3%1.6%0.1%12
98.3%1.6%0.1%13
99.1%0.8%0.1%14
Compiler

Compiled 8 to 8 computations (0% saved)

sample15.0ms (0.1%)

Algorithm
intervals
Results
5.0ms238×body128valid
1.0msbody512valid
0.0msbody2048valid
0.0msbody1024valid
0.0msbody256valid
Compiler

Compiled 15 to 17 computations (-13.3% saved)

simplify1.1s (10.7%)

Algorithm
egg-herbie
Rules
858×exp-prod_binary64_10360
820×swap-sqr_binary64_10275
263×associate-/l*_binary64_10253
258×distribute-rgt-out_binary64_10261
255×associate-*r*_binary64_10248
227×sub-neg_binary64_10301
207×distribute-rgt-out--_binary64_10262
191×associate-/l/_binary64_10255
145×associate-*l*_binary64_10249
140×cancel-sign-sub-inv_binary64_10274
76×distribute-lft-out_binary64_10259
72×distribute-lft-out--_binary64_10260
57×times-frac_binary64_10314
53×associate-/r*_binary64_10252
48×div-sub_binary64_10313
31×associate-*l/_binary64_10251 associate-*r/_binary64_10250
29×unsub-neg_binary64_10302
25×neg-mul-1_binary64_10304 distribute-lft-neg-in_binary64_10265
24×associate-/r/_binary64_10254
23×neg-sub0_binary64_10303
22×distribute-rgt-neg-in_binary64_10266 distribute-rgt-in_binary64_10258
21×*-commutative_binary64_10239
15×distribute-rgt1-in_binary64_10264
14×+-inverses_binary64_10287
13×+-commutative_binary64_10238
12×distribute-neg-frac_binary64_10272
10×associate-+l-_binary64_10243
associate--r+_binary64_10244
sub0-neg_binary64_10295 --rgt-identity_binary64_10294
distribute-neg-in_binary64_10269
distribute-lft-in_binary64_10257 associate-+r-_binary64_10242
cube-unmult_binary64_10345 remove-double-neg_binary64_10296 +-lft-identity_binary64_10292 mul0-lft_binary64_10290
+-rgt-identity_binary64_10293 unswap-sqr_binary64_10276 associate-+l+_binary64_10241 associate-+r+_binary64_10240
mul0-rgt_binary64_10291 div0_binary64_10289 distribute-lft-neg-out_binary64_10267 distribute-lft1-in_binary64_10263 count-2_binary64_10256
exp-sum_binary64_10354 difference-of-squares_binary64_10277 associate--r-_binary64_10247
exp-lft-cube_binary64_10364 exp-lft-sqr_binary64_10363 exp-diff_binary64_10356 1-exp_binary64_10352 sqr-neg_binary64_10322 distribute-rgt-neg-out_binary64_10268 associate--l+_binary64_10245
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_10571 erf-erfc_binary64_10570 erf-odd_binary64_10569 if-if-and-not_binary64_10568 if-if-and_binary64_10567 if-if-or-not_binary64_10566 if-if-or_binary64_10565 if-not_binary64_10564 if-same_binary64_10563 if-false_binary64_10562 if-true_binary64_10561 not-gte_binary64_10560 not-lte_binary64_10559 not-gt_binary64_10558 not-lt_binary64_10557 gte-same_binary64_10556 lte-same_binary64_10555 gt-same_binary64_10554 lt-same_binary64_10553 sinh---cosh_binary64_10500 sinh-+-cosh_binary64_10499 sinh-cosh_binary64_10498 tanh-def-c_binary64_10497 tanh-def-b_binary64_10496 tanh-def-a_binary64_10495 cosh-def_binary64_10494 sinh-def_binary64_10493 tan-neg_binary64_10440 cos-neg_binary64_10439 sin-neg_binary64_10438 tan-0_binary64_10437 cos-0_binary64_10436 sin-0_binary64_10435 hang-m-tan_binary64_10434 hang-p-tan_binary64_10433 hang-m0-tan_binary64_10432 hang-p0-tan_binary64_10431 hang-0m-tan_binary64_10430 hang-0p-tan_binary64_10429 tan-+PI/2_binary64_10428 tan-+PI_binary64_10427 tan-PI_binary64_10426 tan-PI/3_binary64_10425 tan-PI/4_binary64_10424 tan-PI/6_binary64_10423 cos-+PI/2_binary64_10422 cos-+PI_binary64_10421 cos-PI_binary64_10420 cos-PI/2_binary64_10419 cos-PI/3_binary64_10418 cos-PI/4_binary64_10417 cos-PI/6_binary64_10416 sin-+PI/2_binary64_10415 sin-+PI_binary64_10414 sin-PI_binary64_10413 sin-PI/2_binary64_10412 sin-PI/3_binary64_10411 sin-PI/4_binary64_10410 sin-PI/6_binary64_10409 sub-1-sin_binary64_10408 sub-1-cos_binary64_10407 -1-add-sin_binary64_10406 -1-add-cos_binary64_10405 1-sub-sin_binary64_10404 1-sub-cos_binary64_10403 cos-sin-sum_binary64_10402 log-E_binary64_10398 log-pow_binary64_10397 log-rec_binary64_10396 log-div_binary64_10395 log-prod_binary64_10394 pow-base-0_binary64_10392 unpow1/3_binary64_10375 unpow3_binary64_10374 unpow2_binary64_10373 unpow1/2_binary64_10372 pow-plus_binary64_10371 exp-to-pow_binary64_10370 pow-base-1_binary64_10368 unpow0_binary64_10367 unpow1_binary64_10366 unpow-1_binary64_10365 exp-cbrt_binary64_10362 exp-sqrt_binary64_10361 div-exp_binary64_10359 rec-exp_binary64_10358 prod-exp_binary64_10357 exp-neg_binary64_10355 e-exp-1_binary64_10353 exp-1-e_binary64_10351 exp-0_binary64_10350 rem-log-exp_binary64_10349 rem-exp-log_binary64_10348 cube-mult_binary64_10338 cube-div_binary64_10337 cube-prod_binary64_10336 cube-neg_binary64_10335 rem-3cbrt-rft_binary64_10334 rem-3cbrt-lft_binary64_10333 rem-cbrt-cube_binary64_10332 rem-cube-cbrt_binary64_10331 sqr-abs_binary64_10323 rem-sqrt-square_binary64_10321 rem-square-sqrt_binary64_10320 mul-1-neg_binary64_10300 /-rgt-identity_binary64_10299 *-rgt-identity_binary64_10298 *-lft-identity_binary64_10297 *-inverses_binary64_10288 lft-mult-inverse_binary64_10286 rgt-mult-inverse_binary64_10285 remove-double-div_binary64_10284 pow-sqr_binary64_10281 sqr-pow_binary64_10280 difference-of-sqr--1_binary64_10279 difference-of-sqr-1_binary64_10278 cancel-sign-sub_binary64_10273 distribute-frac-neg_binary64_10271 distribute-neg-out_binary64_10270 associate--l-_binary64_10246
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11610
23310
35610
49210
513510
625210
7242110

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
0.1b
Counts
2 → 1
Compiler

Compiled 14 to 14 computations (0% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b
(-.f64 x (*.f64 (/.f64 3 8) y))

rewrite17.0ms (0.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
add-log-exp_binary64_10347
diff-log_binary64_10400 pow1_binary64_10369 add-exp-log_binary64_10346 add-cbrt-cube_binary64_10344 add-cube-cbrt_binary64_10343 add-sqr-sqrt_binary64_10330 flip3--_binary64_10312 *-un-lft-identity_binary64_10308 sub-neg_binary64_10301 flip--_binary64_10283 cancel-sign-sub-inv_binary64_10274
Counts
1 → 12
Calls

1 calls:

3.0ms
(-.f64 x (*.f64 (/.f64 3 8) y))
Compiler

Compiled 187 to 144 computations (23% saved)

series100.0ms (1%)

Error
0.1b
Counts
1 → 12
Calls

1 calls:

93.0ms
(-.f64 x (*.f64 (/.f64 3 8) y))
Compiler

Compiled 114 to 104 computations (8.8% saved)

simplify94.0ms (0.9%)

Algorithm
egg-herbie
Rules
536×times-frac_binary64_10314
503×associate-*l/_binary64_10251
374×associate-*r/_binary64_10250
348×distribute-neg-frac_binary64_10272
280×unsub-neg_binary64_10302
269×distribute-lft-neg-out_binary64_10267
256×distribute-rgt-neg-out_binary64_10268
216×distribute-rgt-in_binary64_10258
196×distribute-rgt-neg-in_binary64_10266
193×associate-/l*_binary64_10253
182×distribute-lft-in_binary64_10257
180×cancel-sign-sub-inv_binary64_10274
130×associate-*l*_binary64_10249
102×associate-*r*_binary64_10248
97×distribute-lft-neg-in_binary64_10265
95×neg-sub0_binary64_10303
93×neg-mul-1_binary64_10304
92×*-commutative_binary64_10239
78×sqr-pow_binary64_10280
73×div-sub_binary64_10313
68×unswap-sqr_binary64_10276
63×sub-neg_binary64_10301
53×distribute-neg-out_binary64_10270
49×distribute-neg-in_binary64_10269
46×pow-sqr_binary64_10281
42×associate-/l/_binary64_10255
40×difference-of-squares_binary64_10277
37×associate-/r*_binary64_10252
32×exp-sum_binary64_10354 associate-/r/_binary64_10254
31×associate-+r+_binary64_10240
30×mul0-rgt_binary64_10291 mul0-lft_binary64_10290
28×exp-prod_binary64_10360
25×swap-sqr_binary64_10275
24×distribute-frac-neg_binary64_10271
21×associate-+l+_binary64_10241 +-commutative_binary64_10238
14×exp-diff_binary64_10356
13×distribute-rgt-out_binary64_10261
10×+-rgt-identity_binary64_10293
unpow3_binary64_10374 cube-mult_binary64_10338
mul-1-neg_binary64_10300
cube-unmult_binary64_10345 sub0-neg_binary64_10295 associate-+l-_binary64_10243 associate-+r-_binary64_10242
cube-div_binary64_10337
cube-prod_binary64_10336
sqr-neg_binary64_10322 distribute-lft-out_binary64_10259 associate--r+_binary64_10244
exp-neg_binary64_10355 --rgt-identity_binary64_10294
pow-plus_binary64_10371 exp-lft-cube_binary64_10364
div-exp_binary64_10359 prod-exp_binary64_10357 1-exp_binary64_10352 cube-neg_binary64_10335 remove-double-neg_binary64_10296 +-lft-identity_binary64_10292 div0_binary64_10289 *-inverses_binary64_10288 cancel-sign-sub_binary64_10273 count-2_binary64_10256
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_10571 erf-erfc_binary64_10570 erf-odd_binary64_10569 if-if-and-not_binary64_10568 if-if-and_binary64_10567 if-if-or-not_binary64_10566 if-if-or_binary64_10565 if-not_binary64_10564 if-same_binary64_10563 if-false_binary64_10562 if-true_binary64_10561 not-gte_binary64_10560 not-lte_binary64_10559 not-gt_binary64_10558 not-lt_binary64_10557 gte-same_binary64_10556 lte-same_binary64_10555 gt-same_binary64_10554 lt-same_binary64_10553 sinh---cosh_binary64_10500 sinh-+-cosh_binary64_10499 sinh-cosh_binary64_10498 tanh-def-c_binary64_10497 tanh-def-b_binary64_10496 tanh-def-a_binary64_10495 cosh-def_binary64_10494 sinh-def_binary64_10493 tan-neg_binary64_10440 cos-neg_binary64_10439 sin-neg_binary64_10438 tan-0_binary64_10437 cos-0_binary64_10436 sin-0_binary64_10435 hang-m-tan_binary64_10434 hang-p-tan_binary64_10433 hang-m0-tan_binary64_10432 hang-p0-tan_binary64_10431 hang-0m-tan_binary64_10430 hang-0p-tan_binary64_10429 tan-+PI/2_binary64_10428 tan-+PI_binary64_10427 tan-PI_binary64_10426 tan-PI/3_binary64_10425 tan-PI/4_binary64_10424 tan-PI/6_binary64_10423 cos-+PI/2_binary64_10422 cos-+PI_binary64_10421 cos-PI_binary64_10420 cos-PI/2_binary64_10419 cos-PI/3_binary64_10418 cos-PI/4_binary64_10417 cos-PI/6_binary64_10416 sin-+PI/2_binary64_10415 sin-+PI_binary64_10414 sin-PI_binary64_10413 sin-PI/2_binary64_10412 sin-PI/3_binary64_10411 sin-PI/4_binary64_10410 sin-PI/6_binary64_10409 sub-1-sin_binary64_10408 sub-1-cos_binary64_10407 -1-add-sin_binary64_10406 -1-add-cos_binary64_10405 1-sub-sin_binary64_10404 1-sub-cos_binary64_10403 cos-sin-sum_binary64_10402 log-E_binary64_10398 log-pow_binary64_10397 log-rec_binary64_10396 log-div_binary64_10395 log-prod_binary64_10394 pow-base-0_binary64_10392 unpow1/3_binary64_10375 unpow2_binary64_10373 unpow1/2_binary64_10372 exp-to-pow_binary64_10370 pow-base-1_binary64_10368 unpow0_binary64_10367 unpow1_binary64_10366 unpow-1_binary64_10365 exp-lft-sqr_binary64_10363 exp-cbrt_binary64_10362 exp-sqrt_binary64_10361 rec-exp_binary64_10358 e-exp-1_binary64_10353 exp-1-e_binary64_10351 exp-0_binary64_10350 rem-log-exp_binary64_10349 rem-exp-log_binary64_10348 rem-3cbrt-rft_binary64_10334 rem-3cbrt-lft_binary64_10333 rem-cbrt-cube_binary64_10332 rem-cube-cbrt_binary64_10331 sqr-abs_binary64_10323 rem-sqrt-square_binary64_10321 rem-square-sqrt_binary64_10320 /-rgt-identity_binary64_10299 *-rgt-identity_binary64_10298 *-lft-identity_binary64_10297 +-inverses_binary64_10287 lft-mult-inverse_binary64_10286 rgt-mult-inverse_binary64_10285 remove-double-div_binary64_10284 difference-of-sqr--1_binary64_10279 difference-of-sqr-1_binary64_10278 distribute-rgt1-in_binary64_10264 distribute-lft1-in_binary64_10263 distribute-rgt-out--_binary64_10262 distribute-lft-out--_binary64_10260 associate--r-_binary64_10247 associate--l-_binary64_10246 associate--l+_binary64_10245
Counts
24 → 62
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
036280
197259
2297259
3964259
43047259

prune80.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New58462
Fresh000
Picked011
Done000
Total58563
Error
0.0b
Counts
63 → 5
Compiler

Compiled 1256 to 932 computations (25.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (neg.f64 (/.f64 3 (/.f64 8 y))))
0.3b
(/.f64 3 (/.f64 8 y))

rewrite156.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
75×times-frac_binary64_10314
48×*-un-lft-identity_binary64_10308
44×add-cube-cbrt_binary64_10343 add-sqr-sqrt_binary64_10330
13×associate-/r*_binary64_10252
add-exp-log_binary64_10346 add-cbrt-cube_binary64_10344
add-log-exp_binary64_10347
div-inv_binary64_10305
div-exp_binary64_10359 cbrt-undiv_binary64_10342 associate-/l*_binary64_10253
pow1_binary64_10369 sum-log_binary64_10399 distribute-lft-out_binary64_10259
frac-2neg_binary64_10319 clear-num_binary64_10307 associate-/r/_binary64_10254 neg-log_binary64_10401 flip3-+_binary64_10311 unsub-neg_binary64_10302 flip-+_binary64_10282 distribute-rgt-neg-in_binary64_10266 neg-sub0_binary64_10303 associate-+r-_binary64_10242 +-commutative_binary64_10238
Counts
2 → 86
Calls

2 calls:

23.0ms
(+.f64 x (neg.f64 (/.f64 3 (/.f64 8 y))))
6.0ms
(/.f64 3 (/.f64 8 y))
Compiler

Compiled 1468 to 1150 computations (21.7% saved)

series120.0ms (1.2%)

Error
0.0b
Counts
2 → 15
Calls

2 calls:

87.0ms
(+.f64 x (neg.f64 (/.f64 3 (/.f64 8 y))))
26.0ms
(/.f64 3 (/.f64 8 y))
Compiler

Compiled 168 to 152 computations (9.5% saved)

simplify268.0ms (2.7%)

Algorithm
egg-herbie
Rules
731×times-frac_binary64_10314
352×associate-/l/_binary64_10255
320×associate-*l/_binary64_10251
309×associate-*l*_binary64_10249
296×associate-/r/_binary64_10254
271×associate-*r*_binary64_10248
256×distribute-rgt-neg-out_binary64_10268
246×associate-/r*_binary64_10252
219×associate-*r/_binary64_10250
205×unsub-neg_binary64_10302
201×distribute-lft-neg-out_binary64_10267
196×distribute-neg-frac_binary64_10272
187×*-commutative_binary64_10239
118×associate-/l*_binary64_10253
114×distribute-rgt-in_binary64_10258
102×div-sub_binary64_10313
93×neg-sub0_binary64_10303
89×distribute-lft-in_binary64_10257
84×cancel-sign-sub-inv_binary64_10274
77×neg-mul-1_binary64_10304
74×cube-prod_binary64_10336
73×unswap-sqr_binary64_10276 distribute-frac-neg_binary64_10271
69×sub-neg_binary64_10301
66×distribute-neg-out_binary64_10270
58×log-prod_binary64_10394 exp-prod_binary64_10360
52×cancel-sign-sub_binary64_10273
51×sqr-pow_binary64_10280
46×distribute-rgt-neg-in_binary64_10266 distribute-lft-neg-in_binary64_10265
37×/-rgt-identity_binary64_10299 swap-sqr_binary64_10275
34×cube-div_binary64_10337
32×*-lft-identity_binary64_10297
29×log-div_binary64_10395 div-exp_binary64_10359 associate-+r+_binary64_10240
28×prod-exp_binary64_10357 distribute-neg-in_binary64_10269
27×*-rgt-identity_binary64_10298
26×pow-sqr_binary64_10281
20×associate-+l-_binary64_10243
19×+-commutative_binary64_10238
18×mul0-lft_binary64_10290 associate-+l+_binary64_10241
16×remove-double-neg_binary64_10296 mul0-rgt_binary64_10291
15×distribute-rgt-out_binary64_10261 associate--r+_binary64_10244
13×exp-sum_binary64_10354
12×unpow3_binary64_10374 sub0-neg_binary64_10295
11×cube-mult_binary64_10338
exp-diff_binary64_10356 cube-neg_binary64_10335 difference-of-squares_binary64_10277
cube-unmult_binary64_10345 sqr-neg_binary64_10322 associate--r-_binary64_10247 associate--l-_binary64_10246 associate--l+_binary64_10245 associate-+r-_binary64_10242
rec-exp_binary64_10358
exp-to-pow_binary64_10370 remove-double-div_binary64_10284 distribute-lft-out_binary64_10259
+-rgt-identity_binary64_10293 distribute-rgt-out--_binary64_10262
log-pow_binary64_10397 pow-plus_binary64_10371 exp-lft-cube_binary64_10364 div0_binary64_10289
exp-neg_binary64_10355 --rgt-identity_binary64_10294
log-rec_binary64_10396 pow-base-1_binary64_10368 1-exp_binary64_10352 rem-log-exp_binary64_10349 mul-1-neg_binary64_10300 count-2_binary64_10256
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_10571 erf-erfc_binary64_10570 erf-odd_binary64_10569 if-if-and-not_binary64_10568 if-if-and_binary64_10567 if-if-or-not_binary64_10566 if-if-or_binary64_10565 if-not_binary64_10564 if-same_binary64_10563 if-false_binary64_10562 if-true_binary64_10561 not-gte_binary64_10560 not-lte_binary64_10559 not-gt_binary64_10558 not-lt_binary64_10557 gte-same_binary64_10556 lte-same_binary64_10555 gt-same_binary64_10554 lt-same_binary64_10553 sinh---cosh_binary64_10500 sinh-+-cosh_binary64_10499 sinh-cosh_binary64_10498 tanh-def-c_binary64_10497 tanh-def-b_binary64_10496 tanh-def-a_binary64_10495 cosh-def_binary64_10494 sinh-def_binary64_10493 tan-neg_binary64_10440 cos-neg_binary64_10439 sin-neg_binary64_10438 tan-0_binary64_10437 cos-0_binary64_10436 sin-0_binary64_10435 hang-m-tan_binary64_10434 hang-p-tan_binary64_10433 hang-m0-tan_binary64_10432 hang-p0-tan_binary64_10431 hang-0m-tan_binary64_10430 hang-0p-tan_binary64_10429 tan-+PI/2_binary64_10428 tan-+PI_binary64_10427 tan-PI_binary64_10426 tan-PI/3_binary64_10425 tan-PI/4_binary64_10424 tan-PI/6_binary64_10423 cos-+PI/2_binary64_10422 cos-+PI_binary64_10421 cos-PI_binary64_10420 cos-PI/2_binary64_10419 cos-PI/3_binary64_10418 cos-PI/4_binary64_10417 cos-PI/6_binary64_10416 sin-+PI/2_binary64_10415 sin-+PI_binary64_10414 sin-PI_binary64_10413 sin-PI/2_binary64_10412 sin-PI/3_binary64_10411 sin-PI/4_binary64_10410 sin-PI/6_binary64_10409 sub-1-sin_binary64_10408 sub-1-cos_binary64_10407 -1-add-sin_binary64_10406 -1-add-cos_binary64_10405 1-sub-sin_binary64_10404 1-sub-cos_binary64_10403 cos-sin-sum_binary64_10402 log-E_binary64_10398 pow-base-0_binary64_10392 unpow1/3_binary64_10375 unpow2_binary64_10373 unpow1/2_binary64_10372 unpow0_binary64_10367 unpow1_binary64_10366 unpow-1_binary64_10365 exp-lft-sqr_binary64_10363 exp-cbrt_binary64_10362 exp-sqrt_binary64_10361 e-exp-1_binary64_10353 exp-1-e_binary64_10351 exp-0_binary64_10350 rem-exp-log_binary64_10348 rem-3cbrt-rft_binary64_10334 rem-3cbrt-lft_binary64_10333 rem-cbrt-cube_binary64_10332 rem-cube-cbrt_binary64_10331 sqr-abs_binary64_10323 rem-sqrt-square_binary64_10321 rem-square-sqrt_binary64_10320 +-lft-identity_binary64_10292 *-inverses_binary64_10288 +-inverses_binary64_10287 lft-mult-inverse_binary64_10286 rgt-mult-inverse_binary64_10285 difference-of-sqr--1_binary64_10279 difference-of-sqr-1_binary64_10278 distribute-rgt1-in_binary64_10264 distribute-lft1-in_binary64_10263 distribute-lft-out--_binary64_10260
Counts
101 → 365
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01811559
14071474
213651467
339071467

prune623.0ms (6.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3623365
Fresh213
Picked101
Done011
Total3655370
Error
0b
Counts
370 → 5
Compiler

Compiled 7193 to 5452 computations (24.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 x (neg.f64 (*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (/.f64 (cbrt.f64 3) 8) y))))
0.3b
(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (/.f64 (cbrt.f64 3) 8) y))
0.4b
(*.f64 (/.f64 (cbrt.f64 3) 8) y)

rewrite171.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
29×add-exp-log_binary64_10346
25×add-sqr-sqrt_binary64_10330
23×associate-*l*_binary64_10249
20×add-cbrt-cube_binary64_10344 times-frac_binary64_10314
19×*-un-lft-identity_binary64_10308
17×pow1_binary64_10369 add-cube-cbrt_binary64_10343
15×prod-exp_binary64_10357 cbrt-unprod_binary64_10341
10×cbrt-prod_binary64_10339
pow-prod-down_binary64_10379
add-log-exp_binary64_10347
associate-*r*_binary64_10248
div-exp_binary64_10359 cbrt-undiv_binary64_10342 unswap-sqr_binary64_10276
associate-*l/_binary64_10251 *-commutative_binary64_10239 sum-log_binary64_10399
div-inv_binary64_10305 associate-*r/_binary64_10250 neg-log_binary64_10401 flip3-+_binary64_10311 unsub-neg_binary64_10302 flip-+_binary64_10282 distribute-lft-out_binary64_10259 neg-sub0_binary64_10303 associate-+r-_binary64_10242 +-commutative_binary64_10238
Counts
3 → 84
Calls

3 calls:

12.0ms
(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (/.f64 (cbrt.f64 3) 8) y))
11.0ms
(*.f64 (/.f64 (cbrt.f64 3) 8) y)
4.0ms
(+.f64 x (neg.f64 (*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (/.f64 (cbrt.f64 3) 8) y))))
Compiler

Compiled 1996 to 1752 computations (12.2% saved)

series473.0ms (4.7%)

Error
0b
Counts
3 → 18
Calls

3 calls:

278.0ms
(+.f64 x (neg.f64 (*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (/.f64 (cbrt.f64 3) 8) y))))
110.0ms
(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (/.f64 (cbrt.f64 3) 8) y))
69.0ms
(*.f64 (/.f64 (cbrt.f64 3) 8) y)
Compiler

Compiled 468 to 446 computations (4.7% saved)

simplify354.0ms (3.5%)

Algorithm
egg-herbie
Rules
481×associate-*r/_binary64_10250
386×associate-*l/_binary64_10251
360×*-commutative_binary64_10239
260×cancel-sign-sub-inv_binary64_10274
201×associate-/l*_binary64_10253
197×neg-mul-1_binary64_10304
184×cube-prod_binary64_10336
182×distribute-rgt-neg-in_binary64_10266
179×associate-*l*_binary64_10249
171×associate-*r*_binary64_10248
167×distribute-lft-neg-in_binary64_10265
145×exp-prod_binary64_10360
119×distribute-rgt-in_binary64_10258
116×log-prod_binary64_10394
97×distribute-lft-in_binary64_10257
71×times-frac_binary64_10314
70×distribute-lft-neg-out_binary64_10267
67×cube-div_binary64_10337
63×distribute-rgt-neg-out_binary64_10268
61×log-div_binary64_10395
56×associate-+r+_binary64_10240
50×associate-/r*_binary64_10252
45×div-sub_binary64_10313 associate-+l+_binary64_10241
43×swap-sqr_binary64_10275
41×neg-sub0_binary64_10303 sqr-pow_binary64_10280
39×distribute-rgt-out_binary64_10261
33×sub-neg_binary64_10301
28×unpow3_binary64_10374 associate-+l-_binary64_10243
24×exp-sum_binary64_10354 cube-mult_binary64_10338 +-commutative_binary64_10238
23×unswap-sqr_binary64_10276
22×unsub-neg_binary64_10302
21×distribute-neg-frac_binary64_10272
20×associate-+r-_binary64_10242
19×associate-/l/_binary64_10255 associate--r+_binary64_10244
15×associate-/r/_binary64_10254
14×exp-diff_binary64_10356 cube-neg_binary64_10335
12×sqr-neg_binary64_10322
11×pow-plus_binary64_10371 pow-sqr_binary64_10281 distribute-lft-out_binary64_10259 associate--r-_binary64_10247
associate--l+_binary64_10245
cube-unmult_binary64_10345
*-rgt-identity_binary64_10298 *-lft-identity_binary64_10297 distribute-rgt-out--_binary64_10262 associate--l-_binary64_10246
remove-double-neg_binary64_10296 distribute-neg-in_binary64_10269
exp-to-pow_binary64_10370 mul0-rgt_binary64_10291 mul0-lft_binary64_10290 distribute-neg-out_binary64_10270
log-pow_binary64_10397 log-rec_binary64_10396
div-exp_binary64_10359 prod-exp_binary64_10357 exp-neg_binary64_10355 +-rgt-identity_binary64_10293 difference-of-squares_binary64_10277 cancel-sign-sub_binary64_10273
rec-exp_binary64_10358 rem-sqrt-square_binary64_10321 /-rgt-identity_binary64_10299 sub0-neg_binary64_10295 --rgt-identity_binary64_10294 distribute-lft-out--_binary64_10260 count-2_binary64_10256
1-exp_binary64_10352 exp-1-e_binary64_10351 rem-log-exp_binary64_10349 rem-cube-cbrt_binary64_10331 distribute-lft1-in_binary64_10263
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_10571 erf-erfc_binary64_10570 erf-odd_binary64_10569 if-if-and-not_binary64_10568 if-if-and_binary64_10567 if-if-or-not_binary64_10566 if-if-or_binary64_10565 if-not_binary64_10564 if-same_binary64_10563 if-false_binary64_10562 if-true_binary64_10561 not-gte_binary64_10560 not-lte_binary64_10559 not-gt_binary64_10558 not-lt_binary64_10557 gte-same_binary64_10556 lte-same_binary64_10555 gt-same_binary64_10554 lt-same_binary64_10553 sinh---cosh_binary64_10500 sinh-+-cosh_binary64_10499 sinh-cosh_binary64_10498 tanh-def-c_binary64_10497 tanh-def-b_binary64_10496 tanh-def-a_binary64_10495 cosh-def_binary64_10494 sinh-def_binary64_10493 tan-neg_binary64_10440 cos-neg_binary64_10439 sin-neg_binary64_10438 tan-0_binary64_10437 cos-0_binary64_10436 sin-0_binary64_10435 hang-m-tan_binary64_10434 hang-p-tan_binary64_10433 hang-m0-tan_binary64_10432 hang-p0-tan_binary64_10431 hang-0m-tan_binary64_10430 hang-0p-tan_binary64_10429 tan-+PI/2_binary64_10428 tan-+PI_binary64_10427 tan-PI_binary64_10426 tan-PI/3_binary64_10425 tan-PI/4_binary64_10424 tan-PI/6_binary64_10423 cos-+PI/2_binary64_10422 cos-+PI_binary64_10421 cos-PI_binary64_10420 cos-PI/2_binary64_10419 cos-PI/3_binary64_10418 cos-PI/4_binary64_10417 cos-PI/6_binary64_10416 sin-+PI/2_binary64_10415 sin-+PI_binary64_10414 sin-PI_binary64_10413 sin-PI/2_binary64_10412 sin-PI/3_binary64_10411 sin-PI/4_binary64_10410 sin-PI/6_binary64_10409 sub-1-sin_binary64_10408 sub-1-cos_binary64_10407 -1-add-sin_binary64_10406 -1-add-cos_binary64_10405 1-sub-sin_binary64_10404 1-sub-cos_binary64_10403 cos-sin-sum_binary64_10402 log-E_binary64_10398 pow-base-0_binary64_10392 unpow1/3_binary64_10375 unpow2_binary64_10373 unpow1/2_binary64_10372 pow-base-1_binary64_10368 unpow0_binary64_10367 unpow1_binary64_10366 unpow-1_binary64_10365 exp-lft-cube_binary64_10364 exp-lft-sqr_binary64_10363 exp-cbrt_binary64_10362 exp-sqrt_binary64_10361 e-exp-1_binary64_10353 exp-0_binary64_10350 rem-exp-log_binary64_10348 rem-3cbrt-rft_binary64_10334 rem-3cbrt-lft_binary64_10333 rem-cbrt-cube_binary64_10332 sqr-abs_binary64_10323 rem-square-sqrt_binary64_10320 mul-1-neg_binary64_10300 +-lft-identity_binary64_10292 div0_binary64_10289 *-inverses_binary64_10288 +-inverses_binary64_10287 lft-mult-inverse_binary64_10286 rgt-mult-inverse_binary64_10285 remove-double-div_binary64_10284 difference-of-sqr--1_binary64_10279 difference-of-sqr-1_binary64_10278 distribute-frac-neg_binary64_10271 distribute-rgt1-in_binary64_10264
Counts
102 → 209
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01401288
13521098
212261088
343991088

prune331.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2090209
Fresh033
Picked011
Done011
Total2095214
Error
0b
Counts
214 → 5
Compiler

Compiled 4112 to 3426 computations (16.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (neg.f64 (*.f64 (sqrt.f64 y) (/.f64 3 (/.f64 8 (sqrt.f64 y))))))
0.1b
(/.f64 3 (/.f64 8 (sqrt.f64 y)))
0.1b
(/.f64 8 (sqrt.f64 y))
0.2b
(*.f64 (sqrt.f64 y) (/.f64 3 (/.f64 8 (sqrt.f64 y))))

rewrite486.0ms (4.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
286×times-frac_binary64_10314
184×add-sqr-sqrt_binary64_10330
160×*-un-lft-identity_binary64_10308
158×add-cube-cbrt_binary64_10343
84×sqrt-prod_binary64_10324
71×associate-*r*_binary64_10248
28×associate-/r*_binary64_10252
20×add-exp-log_binary64_10346 add-cbrt-cube_binary64_10344
10×div-inv_binary64_10305
add-log-exp_binary64_10347 unswap-sqr_binary64_10276
div-exp_binary64_10359 cbrt-undiv_binary64_10342
pow1_binary64_10369 associate-*l*_binary64_10249 associate-/l*_binary64_10253
prod-exp_binary64_10357 cbrt-unprod_binary64_10341
associate-/r/_binary64_10254 frac-2neg_binary64_10319 clear-num_binary64_10307 sum-log_binary64_10399
pow-prod-down_binary64_10379 associate-*r/_binary64_10250 *-commutative_binary64_10239 neg-log_binary64_10401 flip3-+_binary64_10311 unsub-neg_binary64_10302 flip-+_binary64_10282 distribute-lft-out_binary64_10259 neg-sub0_binary64_10303 associate-+r-_binary64_10242 +-commutative_binary64_10238
Counts
4 → 261
Calls

4 calls:

27.0ms
(*.f64 (sqrt.f64 y) (/.f64 3 (/.f64 8 (sqrt.f64 y))))
8.0ms
(/.f64 3 (/.f64 8 (sqrt.f64 y)))
4.0ms
(/.f64 8 (sqrt.f64 y))
4.0ms
(+.f64 x (neg.f64 (*.f64 (sqrt.f64 y) (/.f64 3 (/.f64 8 (sqrt.f64 y))))))
Compiler

Compiled 5965 to 3825 computations (35.9% saved)

series175.0ms (1.7%)

Error
0b
Counts
4 → 20
Calls

4 calls:

87.0ms
(+.f64 x (neg.f64 (*.f64 (sqrt.f64 y) (/.f64 3 (/.f64 8 (sqrt.f64 y))))))
28.0ms
(*.f64 (sqrt.f64 y) (/.f64 3 (/.f64 8 (sqrt.f64 y))))
26.0ms
(/.f64 3 (/.f64 8 (sqrt.f64 y)))
23.0ms
(/.f64 8 (sqrt.f64 y))
Compiler

Compiled 434 to 378 computations (12.9% saved)

simplify649.0ms (6.5%)

Algorithm
egg-herbie
Rules
339×unsub-neg_binary64_10302
272×associate-/r/_binary64_10254
268×associate-/l*_binary64_10253
257×associate-/l/_binary64_10255 associate-*l*_binary64_10249
230×associate-*l/_binary64_10251
215×associate-*r*_binary64_10248
194×associate-*r/_binary64_10250
188×*-commutative_binary64_10239
181×neg-sub0_binary64_10303
173×neg-mul-1_binary64_10304
166×cancel-sign-sub-inv_binary64_10274
134×div-sub_binary64_10313
132×distribute-rgt-in_binary64_10258
106×distribute-rgt-neg-in_binary64_10266 distribute-lft-in_binary64_10257
104×cube-prod_binary64_10336
91×exp-prod_binary64_10360
90×distribute-lft-neg-in_binary64_10265
84×log-prod_binary64_10394
78×times-frac_binary64_10314
74×*-rgt-identity_binary64_10298
67×distribute-lft-neg-out_binary64_10267
60×distribute-rgt-neg-out_binary64_10268
59×distribute-neg-frac_binary64_10272
58×associate-/r*_binary64_10252
53×cube-div_binary64_10337
52×log-div_binary64_10395
51×*-lft-identity_binary64_10297
40×sub-neg_binary64_10301
38×associate-+r+_binary64_10240
36×/-rgt-identity_binary64_10299
34×sqr-pow_binary64_10280
33×distribute-rgt-out_binary64_10261 associate-+l+_binary64_10241
30×associate-+l-_binary64_10243
29×exp-sum_binary64_10354
28×div-exp_binary64_10359 swap-sqr_binary64_10275
27×prod-exp_binary64_10357 +-commutative_binary64_10238
25×unswap-sqr_binary64_10276
24×unpow3_binary64_10374
22×cube-mult_binary64_10338
19×associate--r+_binary64_10244
18×exp-diff_binary64_10356
14×associate--l+_binary64_10245
13×cube-neg_binary64_10335
11×distribute-lft-out_binary64_10259
10×pow-sqr_binary64_10281 associate--r-_binary64_10247 associate--l-_binary64_10246
sqr-neg_binary64_10322 associate-+r-_binary64_10242
cube-unmult_binary64_10345
remove-double-neg_binary64_10296 distribute-neg-in_binary64_10269 distribute-rgt-out--_binary64_10262
rec-exp_binary64_10358
pow-plus_binary64_10371 exp-to-pow_binary64_10370 rem-sqrt-square_binary64_10321 mul0-rgt_binary64_10291 mul0-lft_binary64_10290 remove-double-div_binary64_10284 distribute-neg-out_binary64_10270
log-pow_binary64_10397 log-rec_binary64_10396 exp-neg_binary64_10355 difference-of-squares_binary64_10277 cancel-sign-sub_binary64_10273
exp-sqrt_binary64_10361 rem-square-sqrt_binary64_10320 sub0-neg_binary64_10295 distribute-lft-out--_binary64_10260 count-2_binary64_10256
unpow2_binary64_10373 pow-base-1_binary64_10368 unpow1_binary64_10366 1-exp_binary64_10352 exp-1-e_binary64_10351 rem-log-exp_binary64_10349 --rgt-identity_binary64_10294 +-rgt-identity_binary64_10293 div0_binary64_10289 *-inverses_binary64_10288 distribute-frac-neg_binary64_10271
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_10571 erf-erfc_binary64_10570 erf-odd_binary64_10569 if-if-and-not_binary64_10568 if-if-and_binary64_10567 if-if-or-not_binary64_10566 if-if-or_binary64_10565 if-not_binary64_10564 if-same_binary64_10563 if-false_binary64_10562 if-true_binary64_10561 not-gte_binary64_10560 not-lte_binary64_10559 not-gt_binary64_10558 not-lt_binary64_10557 gte-same_binary64_10556 lte-same_binary64_10555 gt-same_binary64_10554 lt-same_binary64_10553 sinh---cosh_binary64_10500 sinh-+-cosh_binary64_10499 sinh-cosh_binary64_10498 tanh-def-c_binary64_10497 tanh-def-b_binary64_10496 tanh-def-a_binary64_10495 cosh-def_binary64_10494 sinh-def_binary64_10493 tan-neg_binary64_10440 cos-neg_binary64_10439 sin-neg_binary64_10438 tan-0_binary64_10437 cos-0_binary64_10436 sin-0_binary64_10435 hang-m-tan_binary64_10434 hang-p-tan_binary64_10433 hang-m0-tan_binary64_10432 hang-p0-tan_binary64_10431 hang-0m-tan_binary64_10430 hang-0p-tan_binary64_10429 tan-+PI/2_binary64_10428 tan-+PI_binary64_10427 tan-PI_binary64_10426 tan-PI/3_binary64_10425 tan-PI/4_binary64_10424 tan-PI/6_binary64_10423 cos-+PI/2_binary64_10422 cos-+PI_binary64_10421 cos-PI_binary64_10420 cos-PI/2_binary64_10419 cos-PI/3_binary64_10418 cos-PI/4_binary64_10417 cos-PI/6_binary64_10416 sin-+PI/2_binary64_10415 sin-+PI_binary64_10414 sin-PI_binary64_10413 sin-PI/2_binary64_10412 sin-PI/3_binary64_10411 sin-PI/4_binary64_10410 sin-PI/6_binary64_10409 sub-1-sin_binary64_10408 sub-1-cos_binary64_10407 -1-add-sin_binary64_10406 -1-add-cos_binary64_10405 1-sub-sin_binary64_10404 1-sub-cos_binary64_10403 cos-sin-sum_binary64_10402 log-E_binary64_10398 pow-base-0_binary64_10392 unpow1/3_binary64_10375 unpow1/2_binary64_10372 unpow0_binary64_10367 unpow-1_binary64_10365 exp-lft-cube_binary64_10364 exp-lft-sqr_binary64_10363 exp-cbrt_binary64_10362 e-exp-1_binary64_10353 exp-0_binary64_10350 rem-exp-log_binary64_10348 rem-3cbrt-rft_binary64_10334 rem-3cbrt-lft_binary64_10333 rem-cbrt-cube_binary64_10332 rem-cube-cbrt_binary64_10331 sqr-abs_binary64_10323 mul-1-neg_binary64_10300 +-lft-identity_binary64_10292 +-inverses_binary64_10287 lft-mult-inverse_binary64_10286 rgt-mult-inverse_binary64_10285 difference-of-sqr--1_binary64_10279 difference-of-sqr-1_binary64_10278 distribute-rgt1-in_binary64_10264 distribute-lft1-in_binary64_10263
Counts
281 → 764
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03335452
17754978
230764875
339714843

prune2.1s (20.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New7640764
Fresh022
Picked011
Done022
Total7645769
Error
0b
Counts
769 → 5
Compiler

Compiled 18547 to 12027 computations (35.2% saved)

regimes616.0ms (6.2%)

Accuracy

Total 0.1b remaining (96.6%)

Threshold costs 0.1b (96.6%)

Compiler

Compiled 5316 to 4982 computations (6.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
sub-neg_binary64_10301 *-commutative_binary64_10239 +-commutative_binary64_10238
neg-mul-1_binary64_10304 neg-sub0_binary64_10303
cancel-sign-sub-inv_binary64_10274 distribute-rgt-neg-in_binary64_10266
distribute-neg-frac_binary64_10272 distribute-lft-neg-out_binary64_10267 distribute-lft-neg-in_binary64_10265
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_10568 if-if-and_binary64_10567 if-if-or-not_binary64_10566 if-if-or_binary64_10565 if-not_binary64_10564 if-same_binary64_10563 if-false_binary64_10562 if-true_binary64_10561 tan-0_binary64_10437 cos-0_binary64_10436 sin-0_binary64_10435 unpow1_binary64_10366 e-exp-1_binary64_10353 1-exp_binary64_10352 exp-1-e_binary64_10351 exp-0_binary64_10350 sqr-abs_binary64_10323 sqr-neg_binary64_10322 unsub-neg_binary64_10302 mul-1-neg_binary64_10300 /-rgt-identity_binary64_10299 *-rgt-identity_binary64_10298 *-lft-identity_binary64_10297 remove-double-neg_binary64_10296 sub0-neg_binary64_10295 --rgt-identity_binary64_10294 +-rgt-identity_binary64_10293 +-lft-identity_binary64_10292 cancel-sign-sub_binary64_10273 distribute-frac-neg_binary64_10271 distribute-neg-out_binary64_10270 distribute-neg-in_binary64_10269 distribute-rgt-neg-out_binary64_10268
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11410
22610
33410
44010
54210
Proof
(- f64 h0 (* f64 (/ f64 3 8) h1))

end0.0ms (0%)

sample2.1s (20.6%)

Algorithm
intervals
Results
172.0ms7440×body128valid
15.0ms199×body1024valid
13.0ms143×body2048valid
7.0ms130×body512valid
3.0ms88×body256valid
Compiler

Compiled 1337 to 1254 computations (6.2% saved)

Profiling

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