Details

analyze1.1s (6.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample36.0ms (0.2%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
3.0ms	74×	body	128	nan
1.0ms	29×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify855.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

514×	`exp-prod_binary64_11724`
475×	`swap-sqr_binary64_11639`
344×	`distribute-rgt-neg-in_binary64_11630`
306×	`*-commutative_binary64_11603`
305×	`exp-sum_binary64_11718`
263×	`distribute-rgt-in_binary64_11622`
261×	`neg-mul-1_binary64_11668`
258×	`neg-sub0_binary64_11667`
174×	`pow-plus_binary64_11735`
168×	`associate-r_binary64_11612`
166×	`distribute-rgt-out_binary64_11625`
156×	`associate-+l+_binary64_11605`
154×	`distribute-rgt1-in_binary64_11628`
147×	`distribute-lft-in_binary64_11621`
144×	`sub-neg_binary64_11665`
136×	`distribute-lft-neg-in_binary64_11629`
129×	`associate--r+_binary64_11608`
128×	`distribute-rgt-out--_binary64_11626`
118×	`associate-+r+_binary64_11604`
116×	`div-sub_binary64_11677`
101×	`associate-l_binary64_11613`
99×	`associate--l+_binary64_11609`
94×	`exp-diff_binary64_11720` `cancel-sign-sub-inv_binary64_11638`
87×	`associate-+l-_binary64_11607`
73×	`+-commutative_binary64_11602`
60×	`distribute-lft-out_binary64_11623`
57×	`associate-+r-_binary64_11606`
56×	`distribute-lft-out--_binary64_11624`
40×	`associate--r-_binary64_11611`
33×	`associate--l-_binary64_11610`
32×	`distribute-lft-neg-out_binary64_11631`
30×	`associate-/l*_binary64_11617`
27×	`unsub-neg_binary64_11666`
25×	`sqr-neg_binary64_11686`
21×	`distribute-rgt-neg-out_binary64_11632`
17×	`exp-lft-sqr_binary64_11727`
16×	`distribute-neg-in_binary64_11633` `associate-/r/_binary64_11618` `associate-/r*_binary64_11616`
14×	`distribute-lft1-in_binary64_11627`
12×	`exp-neg_binary64_11719`
11×	`+-inverses_binary64_11651` `count-2_binary64_11620`
7×	`cube-prod_binary64_11700`
6×	`cube-unmult_binary64_11709` `remove-double-neg_binary64_11660` `sub0-neg_binary64_11659` `mul0-lft_binary64_11654` `distribute-neg-out_binary64_11634`
5×	`--rgt-identity_binary64_11658`
4×	`+-rgt-identity_binary64_11657` `+-lft-identity_binary64_11656` `mul0-rgt_binary64_11655` `distribute-frac-neg_binary64_11635`
3×	`unswap-sqr_binary64_11640`
2×	`cube-neg_binary64_11699` `difference-of-squares_binary64_11641` `associate-/l/_binary64_11619`
1×	`1-exp_binary64_11716`
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_11935` `erf-erfc_binary64_11934` `erf-odd_binary64_11933` `if-if-and-not_binary64_11932` `if-if-and_binary64_11931` `if-if-or-not_binary64_11930` `if-if-or_binary64_11929` `if-not_binary64_11928` `if-same_binary64_11927` `if-false_binary64_11926` `if-true_binary64_11925` `not-gte_binary64_11924` `not-lte_binary64_11923` `not-gt_binary64_11922` `not-lt_binary64_11921` `gte-same_binary64_11920` `lte-same_binary64_11919` `gt-same_binary64_11918` `lt-same_binary64_11917` `sinh---cosh_binary64_11864` `sinh-+-cosh_binary64_11863` `sinh-cosh_binary64_11862` `tanh-def-c_binary64_11861` `tanh-def-b_binary64_11860` `tanh-def-a_binary64_11859` `cosh-def_binary64_11858` `sinh-def_binary64_11857` `tan-neg_binary64_11804` `cos-neg_binary64_11803` `sin-neg_binary64_11802` `tan-0_binary64_11801` `cos-0_binary64_11800` `sin-0_binary64_11799` `hang-m-tan_binary64_11798` `hang-p-tan_binary64_11797` `hang-m0-tan_binary64_11796` `hang-p0-tan_binary64_11795` `hang-0m-tan_binary64_11794` `hang-0p-tan_binary64_11793` `tan-+PI/2_binary64_11792` `tan-+PI_binary64_11791` `tan-PI_binary64_11790` `tan-PI/3_binary64_11789` `tan-PI/4_binary64_11788` `tan-PI/6_binary64_11787` `cos-+PI/2_binary64_11786` `cos-+PI_binary64_11785` `cos-PI_binary64_11784` `cos-PI/2_binary64_11783` `cos-PI/3_binary64_11782` `cos-PI/4_binary64_11781` `cos-PI/6_binary64_11780` `sin-+PI/2_binary64_11779` `sin-+PI_binary64_11778` `sin-PI_binary64_11777` `sin-PI/2_binary64_11776` `sin-PI/3_binary64_11775` `sin-PI/4_binary64_11774` `sin-PI/6_binary64_11773` `sub-1-sin_binary64_11772` `sub-1-cos_binary64_11771` `-1-add-sin_binary64_11770` `-1-add-cos_binary64_11769` `1-sub-sin_binary64_11768` `1-sub-cos_binary64_11767` `cos-sin-sum_binary64_11766` `log-E_binary64_11762` `log-pow_binary64_11761` `log-rec_binary64_11760` `log-div_binary64_11759` `log-prod_binary64_11758` `pow-base-0_binary64_11756` `unpow1/3_binary64_11739` `unpow3_binary64_11738` `unpow2_binary64_11737` `unpow1/2_binary64_11736` `exp-to-pow_binary64_11734` `pow-base-1_binary64_11732` `unpow0_binary64_11731` `unpow1_binary64_11730` `unpow-1_binary64_11729` `exp-lft-cube_binary64_11728` `exp-cbrt_binary64_11726` `exp-sqrt_binary64_11725` `div-exp_binary64_11723` `rec-exp_binary64_11722` `prod-exp_binary64_11721` `e-exp-1_binary64_11717` `exp-1-e_binary64_11715` `exp-0_binary64_11714` `rem-log-exp_binary64_11713` `rem-exp-log_binary64_11712` `cube-mult_binary64_11702` `cube-div_binary64_11701` `rem-3cbrt-rft_binary64_11698` `rem-3cbrt-lft_binary64_11697` `rem-cbrt-cube_binary64_11696` `rem-cube-cbrt_binary64_11695` `sqr-abs_binary64_11687` `rem-sqrt-square_binary64_11685` `rem-square-sqrt_binary64_11684` `times-frac_binary64_11678` `mul-1-neg_binary64_11664` `/-rgt-identity_binary64_11663` `-rgt-identity_binary64_11662` `-lft-identity_binary64_11661` `div0_binary64_11653` `-inverses_binary64_11652` `lft-mult-inverse_binary64_11650` `rgt-mult-inverse_binary64_11649` `remove-double-div_binary64_11648` `pow-sqr_binary64_11645` `sqr-pow_binary64_11644` `difference-of-sqr--1_binary64_11643` `difference-of-sqr-1_binary64_11642` `cancel-sign-sub_binary64_11637` `distribute-neg-frac_binary64_11636` `associate-l/_binary64_11615` `associate-*r/_binary64_11614`

Counts

1 → 6

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	25	21
2	51	21
3	81	21
4	122	21
5	143	21
6	222	21
7	1181	21
8	3794	21

prune14.0ms (0.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	2	4	6
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	2	5	7

Error

21.1b

Counts

7 → 5

Compiler

Compiled 154 to 83 computations (46.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
0.2b	(-.f64 (.f64 z z) (.f64 t a))
2.9b	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
25.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite211.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

20.8b

Rules

76×	`times-frac_binary64_11678`
47×	`add-sqr-sqrt_binary64_11694`
46×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
33×	`sqrt-prod_binary64_11688`
25×	`associate-/r*_binary64_11616`
18×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
7×	`div-exp_binary64_11723` `cbrt-undiv_binary64_11706` `associate-/l*_binary64_11617`
6×	`add-log-exp_binary64_11711`
5×	`pow1_binary64_11733`
4×	`sqrt-div_binary64_11689` `div-inv_binary64_11669`
3×	`flip3--_binary64_11676` `flip--_binary64_11647`
2×	`prod-exp_binary64_11721` `cbrt-unprod_binary64_11705` `frac-2neg_binary64_11683` `clear-num_binary64_11671` `associate-/l/_binary64_11619`
1×	`pow1/2_binary64_11752` `sqrt-pow1_binary64_11690` `rem-sqrt-square_binary64_11685` `associate-/r/_binary64_11618` `diff-log_binary64_11764` `sub-neg_binary64_11665` `cancel-sign-sub-inv_binary64_11638`

Counts

4 → 132

Calls

4 calls:

11.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
8.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 3488 to 515 computations (85.2% saved)

series1.4s (7.7%)

Error

2.5b

Counts

4 → 81

Calls

4 calls:

653.0ms	(/.f64 (.f64 x y) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
253.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
201.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
195.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 3629 to 2656 computations (26.8% saved)

simplify508.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

274×	`associate-/l*_binary64_11617`
215×	`neg-mul-1_binary64_11668`
211×	`div-sub_binary64_11677`
200×	`times-frac_binary64_11678`
194×	`associate-l_binary64_11613`
186×	`associate-r_binary64_11612`
167×	`cancel-sign-sub-inv_binary64_11638`
164×	`distribute-rgt-neg-in_binary64_11630`
154×	`associate-/l/_binary64_11619`
148×	`distribute-neg-frac_binary64_11636`
145×	`associate-/r/_binary64_11618`
144×	`distribute-lft-neg-in_binary64_11629`
134×	`associate-*l/_binary64_11615`
128×	`*-commutative_binary64_11603`
112×	`associate-/r*_binary64_11616`
94×	`sub-neg_binary64_11665`
79×	`associate-*r/_binary64_11614`
76×	`+-commutative_binary64_11602`
61×	`sqr-pow_binary64_11644`
58×	`neg-sub0_binary64_11667` `associate-+l+_binary64_11605`
57×	`distribute-rgt-in_binary64_11622`
52×	`log-div_binary64_11759`
48×	`cube-prod_binary64_11700`
47×	`/-rgt-identity_binary64_11663`
45×	`*-rgt-identity_binary64_11662`
44×	`cube-div_binary64_11701` `unswap-sqr_binary64_11640`
43×	`log-prod_binary64_11758`
41×	`exp-prod_binary64_11724`
39×	`distribute-lft-in_binary64_11621` `associate-+r+_binary64_11604`
38×	`associate-+l-_binary64_11607`
34×	`associate--r+_binary64_11608`
30×	`pow-plus_binary64_11735` `associate-+r-_binary64_11606`
29×	`pow-sqr_binary64_11645`
26×	`*-lft-identity_binary64_11661` `distribute-neg-in_binary64_11633`
23×	`distribute-lft-neg-out_binary64_11631` `associate--l+_binary64_11609`
20×	`unpow3_binary64_11738`
18×	`associate--l-_binary64_11610`
17×	`cube-mult_binary64_11702` `unsub-neg_binary64_11666`
14×	`exp-sum_binary64_11718`
13×	`distribute-rgt-out_binary64_11625`
12×	`swap-sqr_binary64_11639`
11×	`cube-unmult_binary64_11709`
10×	`div-exp_binary64_11723`
9×	`prod-exp_binary64_11721` `exp-diff_binary64_11720` `difference-of-squares_binary64_11641`
8×	`associate--r-_binary64_11611`
6×	`mul-1-neg_binary64_11664`
4×	`rem-sqrt-square_binary64_11685` `distribute-rgt-neg-out_binary64_11632` `distribute-lft-out_binary64_11623`
3×	`log-pow_binary64_11761` `log-rec_binary64_11760` `unpow2_binary64_11737` `unpow1_binary64_11730` `rec-exp_binary64_11722` `+-rgt-identity_binary64_11657`
2×	`*-inverses_binary64_11652`
1×	`exp-sqrt_binary64_11725` `1-exp_binary64_11716` `rem-log-exp_binary64_11713` `sqr-neg_binary64_11686` `rem-square-sqrt_binary64_11684` `remove-double-neg_binary64_11660` `sub0-neg_binary64_11659` `div0_binary64_11653` `cancel-sign-sub_binary64_11637` `count-2_binary64_11620`
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_11935` `erf-erfc_binary64_11934` `erf-odd_binary64_11933` `if-if-and-not_binary64_11932` `if-if-and_binary64_11931` `if-if-or-not_binary64_11930` `if-if-or_binary64_11929` `if-not_binary64_11928` `if-same_binary64_11927` `if-false_binary64_11926` `if-true_binary64_11925` `not-gte_binary64_11924` `not-lte_binary64_11923` `not-gt_binary64_11922` `not-lt_binary64_11921` `gte-same_binary64_11920` `lte-same_binary64_11919` `gt-same_binary64_11918` `lt-same_binary64_11917` `sinh---cosh_binary64_11864` `sinh-+-cosh_binary64_11863` `sinh-cosh_binary64_11862` `tanh-def-c_binary64_11861` `tanh-def-b_binary64_11860` `tanh-def-a_binary64_11859` `cosh-def_binary64_11858` `sinh-def_binary64_11857` `tan-neg_binary64_11804` `cos-neg_binary64_11803` `sin-neg_binary64_11802` `tan-0_binary64_11801` `cos-0_binary64_11800` `sin-0_binary64_11799` `hang-m-tan_binary64_11798` `hang-p-tan_binary64_11797` `hang-m0-tan_binary64_11796` `hang-p0-tan_binary64_11795` `hang-0m-tan_binary64_11794` `hang-0p-tan_binary64_11793` `tan-+PI/2_binary64_11792` `tan-+PI_binary64_11791` `tan-PI_binary64_11790` `tan-PI/3_binary64_11789` `tan-PI/4_binary64_11788` `tan-PI/6_binary64_11787` `cos-+PI/2_binary64_11786` `cos-+PI_binary64_11785` `cos-PI_binary64_11784` `cos-PI/2_binary64_11783` `cos-PI/3_binary64_11782` `cos-PI/4_binary64_11781` `cos-PI/6_binary64_11780` `sin-+PI/2_binary64_11779` `sin-+PI_binary64_11778` `sin-PI_binary64_11777` `sin-PI/2_binary64_11776` `sin-PI/3_binary64_11775` `sin-PI/4_binary64_11774` `sin-PI/6_binary64_11773` `sub-1-sin_binary64_11772` `sub-1-cos_binary64_11771` `-1-add-sin_binary64_11770` `-1-add-cos_binary64_11769` `1-sub-sin_binary64_11768` `1-sub-cos_binary64_11767` `cos-sin-sum_binary64_11766` `log-E_binary64_11762` `pow-base-0_binary64_11756` `unpow1/3_binary64_11739` `unpow1/2_binary64_11736` `exp-to-pow_binary64_11734` `pow-base-1_binary64_11732` `unpow0_binary64_11731` `unpow-1_binary64_11729` `exp-lft-cube_binary64_11728` `exp-lft-sqr_binary64_11727` `exp-cbrt_binary64_11726` `exp-neg_binary64_11719` `e-exp-1_binary64_11717` `exp-1-e_binary64_11715` `exp-0_binary64_11714` `rem-exp-log_binary64_11712` `cube-neg_binary64_11699` `rem-3cbrt-rft_binary64_11698` `rem-3cbrt-lft_binary64_11697` `rem-cbrt-cube_binary64_11696` `rem-cube-cbrt_binary64_11695` `sqr-abs_binary64_11687` `--rgt-identity_binary64_11658` `+-lft-identity_binary64_11656` `mul0-rgt_binary64_11655` `mul0-lft_binary64_11654` `+-inverses_binary64_11651` `lft-mult-inverse_binary64_11650` `rgt-mult-inverse_binary64_11649` `remove-double-div_binary64_11648` `difference-of-sqr--1_binary64_11643` `difference-of-sqr-1_binary64_11642` `distribute-frac-neg_binary64_11635` `distribute-neg-out_binary64_11634` `distribute-rgt1-in_binary64_11628` `distribute-lft1-in_binary64_11627` `distribute-rgt-out--_binary64_11626` `distribute-lft-out--_binary64_11624`

Counts

213 → 500

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	5146
1	766	4833
2	3138	4821
3	4306	4821

prune566.0ms (3.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	491	9	500
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	495	10	505

Error

2.5b

Counts

505 → 10

Compiler

Compiled 13048 to 2264 computations (82.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 z z) (.f64 t a))
1.5b	(.f64 x (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
1.7b	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
25.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite579.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

263×	`times-frac_binary64_11678`
157×	`add-sqr-sqrt_binary64_11694`
143×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
71×	`associate-r_binary64_11612`
67×	`sqrt-prod_binary64_11688`
22×	`associate-/r*_binary64_11616`
18×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
9×	`div-inv_binary64_11669`
7×	`pow1_binary64_11733`
6×	`add-log-exp_binary64_11711` `div-exp_binary64_11723` `cbrt-undiv_binary64_11706`
4×	`unswap-sqr_binary64_11640`
3×	`associate-/l_binary64_11617` `prod-exp_binary64_11721` `cbrt-unprod_binary64_11705` `associate-l*_binary64_11613`
2×	`flip3--_binary64_11676` `sqrt-div_binary64_11689` `flip--_binary64_11647` `associate-/r/_binary64_11618`
1×	`pow1/2_binary64_11752` `sqrt-pow1_binary64_11690` `rem-sqrt-square_binary64_11685` `frac-2neg_binary64_11683` `clear-num_binary64_11671` `pow-prod-down_binary64_11743` `associate-r/_binary64_11614` `-commutative_binary64_11603` `diff-log_binary64_11764` `sub-neg_binary64_11665` `cancel-sign-sub-inv_binary64_11638`

Counts

4 → 227

Calls

4 calls:

32.0ms	(.f64 x (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
10.0ms	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 6767 to 1032 computations (84.7% saved)

series1.5s (8.4%)

Error

2.5b

Counts

4 → 78

Calls

4 calls:

638.0ms	(.f64 x (/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z)))
413.0ms	(/.f64 y (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z))
205.0ms	(-.f64 (.f64 z z) (.f64 t a))
186.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 3528 to 2619 computations (25.8% saved)

simplify743.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

382×	`associate-/l*_binary64_11617`
360×	`associate-r_binary64_11612`
356×	`associate-l_binary64_11613`
272×	`associate-/r/_binary64_11618`
262×	`*-commutative_binary64_11603`
260×	`associate-*l/_binary64_11615`
232×	`associate-/l/_binary64_11619`
228×	`associate-*r/_binary64_11614`
209×	`times-frac_binary64_11678`
165×	`distribute-rgt-neg-in_binary64_11630`
144×	`distribute-lft-neg-in_binary64_11629`
136×	`distribute-neg-frac_binary64_11636`
126×	`cancel-sign-sub-inv_binary64_11638`
124×	`associate-/r*_binary64_11616`
89×	`*-rgt-identity_binary64_11662`
67×	`sqr-pow_binary64_11644`
66×	`unswap-sqr_binary64_11640`
65×	`*-lft-identity_binary64_11661`
62×	`sub-neg_binary64_11665`
59×	`neg-sub0_binary64_11667`
53×	`neg-mul-1_binary64_11668`
52×	`distribute-rgt-in_binary64_11622`
45×	`/-rgt-identity_binary64_11663`
40×	`+-commutative_binary64_11602`
31×	`pow-sqr_binary64_11645`
27×	`div-sub_binary64_11677`
25×	`exp-prod_binary64_11724`
22×	`associate-+l+_binary64_11605` `associate-+r+_binary64_11604`
18×	`log-div_binary64_11759` `distribute-lft-neg-out_binary64_11631`
17×	`log-prod_binary64_11758` `pow-plus_binary64_11735` `div-exp_binary64_11723`
16×	`prod-exp_binary64_11721` `distribute-neg-in_binary64_11633`
13×	`cube-prod_binary64_11700` `mul-1-neg_binary64_11664` `distribute-rgt-out_binary64_11625` `associate--r+_binary64_11608`
10×	`unsub-neg_binary64_11666` `swap-sqr_binary64_11639`
9×	`cube-unmult_binary64_11709` `cube-div_binary64_11701` `difference-of-squares_binary64_11641`
6×	`unpow3_binary64_11738`
5×	`cube-mult_binary64_11702`
4×	`rec-exp_binary64_11722` `exp-sum_binary64_11718` `rem-sqrt-square_binary64_11685` `distribute-rgt-neg-out_binary64_11632` `distribute-lft-out_binary64_11623` `distribute-lft-in_binary64_11621`
3×	`unpow2_binary64_11737` `unpow1_binary64_11730` `remove-double-div_binary64_11648` `associate--l+_binary64_11609` `associate-+r-_binary64_11606`
2×	`log-rec_binary64_11760` `exp-diff_binary64_11720` `+-rgt-identity_binary64_11657` `*-inverses_binary64_11652` `associate--r-_binary64_11611`
1×	`log-pow_binary64_11761` `exp-sqrt_binary64_11725` `1-exp_binary64_11716` `exp-1-e_binary64_11715` `rem-log-exp_binary64_11713` `rem-square-sqrt_binary64_11684` `remove-double-neg_binary64_11660` `associate-+l-_binary64_11607`
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_11935` `erf-erfc_binary64_11934` `erf-odd_binary64_11933` `if-if-and-not_binary64_11932` `if-if-and_binary64_11931` `if-if-or-not_binary64_11930` `if-if-or_binary64_11929` `if-not_binary64_11928` `if-same_binary64_11927` `if-false_binary64_11926` `if-true_binary64_11925` `not-gte_binary64_11924` `not-lte_binary64_11923` `not-gt_binary64_11922` `not-lt_binary64_11921` `gte-same_binary64_11920` `lte-same_binary64_11919` `gt-same_binary64_11918` `lt-same_binary64_11917` `sinh---cosh_binary64_11864` `sinh-+-cosh_binary64_11863` `sinh-cosh_binary64_11862` `tanh-def-c_binary64_11861` `tanh-def-b_binary64_11860` `tanh-def-a_binary64_11859` `cosh-def_binary64_11858` `sinh-def_binary64_11857` `tan-neg_binary64_11804` `cos-neg_binary64_11803` `sin-neg_binary64_11802` `tan-0_binary64_11801` `cos-0_binary64_11800` `sin-0_binary64_11799` `hang-m-tan_binary64_11798` `hang-p-tan_binary64_11797` `hang-m0-tan_binary64_11796` `hang-p0-tan_binary64_11795` `hang-0m-tan_binary64_11794` `hang-0p-tan_binary64_11793` `tan-+PI/2_binary64_11792` `tan-+PI_binary64_11791` `tan-PI_binary64_11790` `tan-PI/3_binary64_11789` `tan-PI/4_binary64_11788` `tan-PI/6_binary64_11787` `cos-+PI/2_binary64_11786` `cos-+PI_binary64_11785` `cos-PI_binary64_11784` `cos-PI/2_binary64_11783` `cos-PI/3_binary64_11782` `cos-PI/4_binary64_11781` `cos-PI/6_binary64_11780` `sin-+PI/2_binary64_11779` `sin-+PI_binary64_11778` `sin-PI_binary64_11777` `sin-PI/2_binary64_11776` `sin-PI/3_binary64_11775` `sin-PI/4_binary64_11774` `sin-PI/6_binary64_11773` `sub-1-sin_binary64_11772` `sub-1-cos_binary64_11771` `-1-add-sin_binary64_11770` `-1-add-cos_binary64_11769` `1-sub-sin_binary64_11768` `1-sub-cos_binary64_11767` `cos-sin-sum_binary64_11766` `log-E_binary64_11762` `pow-base-0_binary64_11756` `unpow1/3_binary64_11739` `unpow1/2_binary64_11736` `exp-to-pow_binary64_11734` `pow-base-1_binary64_11732` `unpow0_binary64_11731` `unpow-1_binary64_11729` `exp-lft-cube_binary64_11728` `exp-lft-sqr_binary64_11727` `exp-cbrt_binary64_11726` `exp-neg_binary64_11719` `e-exp-1_binary64_11717` `exp-0_binary64_11714` `rem-exp-log_binary64_11712` `cube-neg_binary64_11699` `rem-3cbrt-rft_binary64_11698` `rem-3cbrt-lft_binary64_11697` `rem-cbrt-cube_binary64_11696` `rem-cube-cbrt_binary64_11695` `sqr-abs_binary64_11687` `sqr-neg_binary64_11686` `sub0-neg_binary64_11659` `--rgt-identity_binary64_11658` `+-lft-identity_binary64_11656` `mul0-rgt_binary64_11655` `mul0-lft_binary64_11654` `div0_binary64_11653` `+-inverses_binary64_11651` `lft-mult-inverse_binary64_11650` `rgt-mult-inverse_binary64_11649` `difference-of-sqr--1_binary64_11643` `difference-of-sqr-1_binary64_11642` `cancel-sign-sub_binary64_11637` `distribute-frac-neg_binary64_11635` `distribute-neg-out_binary64_11634` `distribute-rgt1-in_binary64_11628` `distribute-lft1-in_binary64_11627` `distribute-rgt-out--_binary64_11626` `distribute-lft-out--_binary64_11624` `count-2_binary64_11620` `associate--l-_binary64_11610`

Counts

305 → 875

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	443	8218
1	1066	7866
2	4467	7863

prune1.0s (5.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	872	3	875
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	877	8	885

Error

2.5b

Counts

885 → 8

Compiler

Compiled 25926 to 3440 computations (86.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 z z) (.f64 t a))
1.7b	(/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
8.1b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)
25.4b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite126.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

18×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
16×	`add-sqr-sqrt_binary64_11694`
13×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
12×	`sqrt-prod_binary64_11688` `associate-l_binary64_11613` `times-frac_binary64_11678`
7×	`pow1_binary64_11733`
6×	`add-log-exp_binary64_11711` `sqrt-div_binary64_11689` `associate-/r*_binary64_11616`
5×	`prod-exp_binary64_11721` `cbrt-unprod_binary64_11705`
4×	`flip3--_binary64_11676` `flip--_binary64_11647` `div-exp_binary64_11723` `cbrt-undiv_binary64_11706` `associate-/r/_binary64_11618`
3×	`associate-r_binary64_11612`
2×	`div-inv_binary64_11669`
1×	`pow1/2_binary64_11752` `sqrt-pow1_binary64_11690` `rem-sqrt-square_binary64_11685` `pow-prod-down_binary64_11743` `unswap-sqr_binary64_11640` `associate-l/_binary64_11615` `-commutative_binary64_11603` `frac-2neg_binary64_11683` `clear-num_binary64_11671` `associate-/l*_binary64_11617` `diff-log_binary64_11764` `sub-neg_binary64_11665` `cancel-sign-sub-inv_binary64_11638`

Counts

4 → 88

Calls

4 calls:

12.0ms	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)
9.0ms	(/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 2197 to 348 computations (84.2% saved)

series1.7s (9.3%)

Error

2.5b

Counts

4 → 81

Calls

4 calls:

646.0ms	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)
587.0ms	(/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
199.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
180.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 3822 to 2751 computations (28% saved)

simplify414.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

563×	`associate-/r/_binary64_11618`
376×	`associate-/l/_binary64_11619`
213×	`associate-r_binary64_11612`
208×	`associate-l_binary64_11613`
206×	`times-frac_binary64_11678` `associate-/l*_binary64_11617`
175×	`distribute-rgt-neg-in_binary64_11630`
156×	`distribute-lft-neg-in_binary64_11629`
147×	`cancel-sign-sub-inv_binary64_11638`
142×	`distribute-neg-frac_binary64_11636`
128×	`associate-*l/_binary64_11615`
118×	`*-commutative_binary64_11603`
106×	`associate-/r*_binary64_11616`
90×	`associate-*r/_binary64_11614`
69×	`sqr-pow_binary64_11644`
63×	`sub-neg_binary64_11665`
55×	`neg-sub0_binary64_11667`
49×	`neg-mul-1_binary64_11668` `distribute-rgt-in_binary64_11622`
48×	`unswap-sqr_binary64_11640`
39×	`distribute-lft-in_binary64_11621`
38×	`+-commutative_binary64_11602`
32×	`pow-sqr_binary64_11645`
31×	`div-sub_binary64_11677`
30×	`log-div_binary64_11759` `*-rgt-identity_binary64_11662`
24×	`associate-+l+_binary64_11605` `associate-+r+_binary64_11604`
23×	`exp-prod_binary64_11724` `cube-div_binary64_11701`
22×	`log-prod_binary64_11758`
18×	`distribute-lft-neg-out_binary64_11631`
17×	`cube-prod_binary64_11700`
16×	`pow-plus_binary64_11735`
15×	`distribute-neg-in_binary64_11633`
13×	`distribute-rgt-out_binary64_11625`
12×	`mul-1-neg_binary64_11664` `swap-sqr_binary64_11639`
11×	`associate--r+_binary64_11608`
10×	`unsub-neg_binary64_11666`
9×	`difference-of-squares_binary64_11641`
8×	`cube-unmult_binary64_11709` `*-lft-identity_binary64_11661`
7×	`associate--l+_binary64_11609`
6×	`unpow3_binary64_11738`
5×	`cube-mult_binary64_11702`
4×	`exp-sum_binary64_11718` `distribute-rgt-neg-out_binary64_11632` `distribute-lft-out_binary64_11623`
3×	`unpow2_binary64_11737` `unpow1_binary64_11730` `/-rgt-identity_binary64_11663`
2×	`exp-diff_binary64_11720` `rem-sqrt-square_binary64_11685` `associate-+l-_binary64_11607` `associate-+r-_binary64_11606`
1×	`log-rec_binary64_11760` `exp-sqrt_binary64_11725` `div-exp_binary64_11723` `prod-exp_binary64_11721` `1-exp_binary64_11716` `exp-1-e_binary64_11715` `rem-log-exp_binary64_11713` `rem-square-sqrt_binary64_11684` `sub0-neg_binary64_11659` `+-rgt-identity_binary64_11657` `div0_binary64_11653` `*-inverses_binary64_11652` `cancel-sign-sub_binary64_11637` `count-2_binary64_11620`
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_11935` `erf-erfc_binary64_11934` `erf-odd_binary64_11933` `if-if-and-not_binary64_11932` `if-if-and_binary64_11931` `if-if-or-not_binary64_11930` `if-if-or_binary64_11929` `if-not_binary64_11928` `if-same_binary64_11927` `if-false_binary64_11926` `if-true_binary64_11925` `not-gte_binary64_11924` `not-lte_binary64_11923` `not-gt_binary64_11922` `not-lt_binary64_11921` `gte-same_binary64_11920` `lte-same_binary64_11919` `gt-same_binary64_11918` `lt-same_binary64_11917` `sinh---cosh_binary64_11864` `sinh-+-cosh_binary64_11863` `sinh-cosh_binary64_11862` `tanh-def-c_binary64_11861` `tanh-def-b_binary64_11860` `tanh-def-a_binary64_11859` `cosh-def_binary64_11858` `sinh-def_binary64_11857` `tan-neg_binary64_11804` `cos-neg_binary64_11803` `sin-neg_binary64_11802` `tan-0_binary64_11801` `cos-0_binary64_11800` `sin-0_binary64_11799` `hang-m-tan_binary64_11798` `hang-p-tan_binary64_11797` `hang-m0-tan_binary64_11796` `hang-p0-tan_binary64_11795` `hang-0m-tan_binary64_11794` `hang-0p-tan_binary64_11793` `tan-+PI/2_binary64_11792` `tan-+PI_binary64_11791` `tan-PI_binary64_11790` `tan-PI/3_binary64_11789` `tan-PI/4_binary64_11788` `tan-PI/6_binary64_11787` `cos-+PI/2_binary64_11786` `cos-+PI_binary64_11785` `cos-PI_binary64_11784` `cos-PI/2_binary64_11783` `cos-PI/3_binary64_11782` `cos-PI/4_binary64_11781` `cos-PI/6_binary64_11780` `sin-+PI/2_binary64_11779` `sin-+PI_binary64_11778` `sin-PI_binary64_11777` `sin-PI/2_binary64_11776` `sin-PI/3_binary64_11775` `sin-PI/4_binary64_11774` `sin-PI/6_binary64_11773` `sub-1-sin_binary64_11772` `sub-1-cos_binary64_11771` `-1-add-sin_binary64_11770` `-1-add-cos_binary64_11769` `1-sub-sin_binary64_11768` `1-sub-cos_binary64_11767` `cos-sin-sum_binary64_11766` `log-E_binary64_11762` `log-pow_binary64_11761` `pow-base-0_binary64_11756` `unpow1/3_binary64_11739` `unpow1/2_binary64_11736` `exp-to-pow_binary64_11734` `pow-base-1_binary64_11732` `unpow0_binary64_11731` `unpow-1_binary64_11729` `exp-lft-cube_binary64_11728` `exp-lft-sqr_binary64_11727` `exp-cbrt_binary64_11726` `rec-exp_binary64_11722` `exp-neg_binary64_11719` `e-exp-1_binary64_11717` `exp-0_binary64_11714` `rem-exp-log_binary64_11712` `cube-neg_binary64_11699` `rem-3cbrt-rft_binary64_11698` `rem-3cbrt-lft_binary64_11697` `rem-cbrt-cube_binary64_11696` `rem-cube-cbrt_binary64_11695` `sqr-abs_binary64_11687` `sqr-neg_binary64_11686` `remove-double-neg_binary64_11660` `--rgt-identity_binary64_11658` `+-lft-identity_binary64_11656` `mul0-rgt_binary64_11655` `mul0-lft_binary64_11654` `+-inverses_binary64_11651` `lft-mult-inverse_binary64_11650` `rgt-mult-inverse_binary64_11649` `remove-double-div_binary64_11648` `difference-of-sqr--1_binary64_11643` `difference-of-sqr-1_binary64_11642` `distribute-frac-neg_binary64_11635` `distribute-neg-out_binary64_11634` `distribute-rgt1-in_binary64_11628` `distribute-lft1-in_binary64_11627` `distribute-rgt-out--_binary64_11626` `distribute-lft-out--_binary64_11624` `associate--r-_binary64_11611` `associate--l-_binary64_11610`

Counts

169 → 343

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	259	3665
1	658	3343
2	2690	3343

prune352.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	343	0	343
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	343	8	351

Error

2.5b

Counts

351 → 8

Compiler

Compiled 8352 to 1715 computations (79.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(/.f64 1 (-.f64 (.f64 z z) (.f64 t a)))
4.7b	(.f64 z (.f64 x y))
9.0b	(.f64 (.f64 z (.f64 x y)) (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 t a)))))
24.7b	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))

rewrite180.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

32×	`add-sqr-sqrt_binary64_11694`
30×	`sqrt-prod_binary64_11688`
29×	`times-frac_binary64_11678` `*-un-lft-identity_binary64_11672`
28×	`add-cube-cbrt_binary64_11707`
22×	`add-exp-log_binary64_11710`
21×	`pow1_binary64_11733`
20×	`add-cbrt-cube_binary64_11708`
19×	`associate-r_binary64_11612`
9×	`pow-prod-down_binary64_11743` `prod-exp_binary64_11721` `cbrt-unprod_binary64_11705`
6×	`associate-/r/_binary64_11618`
4×	`add-log-exp_binary64_11711` `associate-l_binary64_11613`
3×	`sqrt-pow1_binary64_11690` `div-inv_binary64_11669` `flip3--_binary64_11676` `flip--_binary64_11647` `rem-sqrt-square_binary64_11685` `associate-/l_binary64_11617` `associate-/r_binary64_11616`
2×	`inv-pow_binary64_11757` `pow-flip_binary64_11746` `sqrt-div_binary64_11689` `*-commutative_binary64_11603` `div-exp_binary64_11723`
1×	`pow1/2_binary64_11752` `associate-*r/_binary64_11614` `1-exp_binary64_11716` `rec-exp_binary64_11722` `cbrt-undiv_binary64_11706` `frac-2neg_binary64_11683` `clear-num_binary64_11671`

Counts

4 → 118

Calls

4 calls:

16.0ms	(.f64 (.f64 z (.f64 x y)) (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 t a)))))
7.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
6.0ms	(/.f64 1 (-.f64 (.f64 z z) (.f64 t a)))
5.0ms	(.f64 z (.f64 x y))

Compiler

Compiled 3104 to 988 computations (68.2% saved)

series1.3s (6.9%)

Error

2.5b

Counts

4 → 70

Calls

4 calls:

631.0ms	(.f64 (.f64 z (.f64 x y)) (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 t a)))))
216.0ms	(sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (.f64 t a))))
189.0ms	(/.f64 1 (-.f64 (.f64 z z) (.f64 t a)))
140.0ms	(.f64 z (.f64 x y))

Compiler

Compiled 3663 to 2668 computations (27.2% saved)

simplify660.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

617×	`associate-/r*_binary64_11616`
417×	`associate-l_binary64_11613`
356×	`associate-r_binary64_11612`
337×	`associate-/r/_binary64_11618`
240×	`associate-/l/_binary64_11619`
141×	`associate-/l*_binary64_11617`
131×	`*-commutative_binary64_11603`
126×	`times-frac_binary64_11678`
120×	`distribute-rgt-neg-in_binary64_11630`
111×	`distribute-lft-neg-in_binary64_11629`
98×	`cancel-sign-sub-inv_binary64_11638`
78×	`sqr-pow_binary64_11644`
74×	`distribute-neg-frac_binary64_11636`
54×	`log-prod_binary64_11758`
52×	`exp-prod_binary64_11724` `unswap-sqr_binary64_11640`
50×	`distribute-rgt-in_binary64_11622`
46×	`distribute-lft-in_binary64_11621`
45×	`cube-prod_binary64_11700`
44×	`neg-sub0_binary64_11667`
43×	`associate-+r+_binary64_11604` `+-commutative_binary64_11602`
42×	`associate-*r/_binary64_11614`
40×	`swap-sqr_binary64_11639`
39×	`neg-mul-1_binary64_11668`
38×	`associate-+l+_binary64_11605`
35×	`distribute-lft-neg-out_binary64_11631`
34×	`pow-sqr_binary64_11645` `associate-*l/_binary64_11615`
30×	`*-rgt-identity_binary64_11662`
27×	`sub-neg_binary64_11665`
22×	`div-sub_binary64_11677` `distribute-rgt-neg-out_binary64_11632`
20×	`*-lft-identity_binary64_11661`
17×	`pow-plus_binary64_11735`
14×	`/-rgt-identity_binary64_11663` `distribute-rgt-out_binary64_11625`
10×	`cube-unmult_binary64_11709` `mul-1-neg_binary64_11664`
9×	`cube-div_binary64_11701` `difference-of-squares_binary64_11641`
7×	`log-div_binary64_11759` `rem-sqrt-square_binary64_11685` `distribute-neg-in_binary64_11633`
6×	`unpow3_binary64_11738` `distribute-frac-neg_binary64_11635`
5×	`cube-mult_binary64_11702` `distribute-neg-out_binary64_11634`
4×	`distribute-lft-out_binary64_11623`
3×	`unpow2_binary64_11737` `unpow1_binary64_11730` `unsub-neg_binary64_11666` `associate--r+_binary64_11608`
2×	`log-rec_binary64_11760` `distribute-rgt-out--_binary64_11626` `count-2_binary64_11620`
1×	`log-pow_binary64_11761` `exp-sqrt_binary64_11725` `div-exp_binary64_11723` `rec-exp_binary64_11722` `prod-exp_binary64_11721` `1-exp_binary64_11716` `exp-1-e_binary64_11715` `rem-log-exp_binary64_11713` `rem-cbrt-cube_binary64_11696` `rem-square-sqrt_binary64_11684` `remove-double-neg_binary64_11660` `div0_binary64_11653` `*-inverses_binary64_11652` `cancel-sign-sub_binary64_11637` `associate--r-_binary64_11611`
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_11935` `erf-erfc_binary64_11934` `erf-odd_binary64_11933` `if-if-and-not_binary64_11932` `if-if-and_binary64_11931` `if-if-or-not_binary64_11930` `if-if-or_binary64_11929` `if-not_binary64_11928` `if-same_binary64_11927` `if-false_binary64_11926` `if-true_binary64_11925` `not-gte_binary64_11924` `not-lte_binary64_11923` `not-gt_binary64_11922` `not-lt_binary64_11921` `gte-same_binary64_11920` `lte-same_binary64_11919` `gt-same_binary64_11918` `lt-same_binary64_11917` `sinh---cosh_binary64_11864` `sinh-+-cosh_binary64_11863` `sinh-cosh_binary64_11862` `tanh-def-c_binary64_11861` `tanh-def-b_binary64_11860` `tanh-def-a_binary64_11859` `cosh-def_binary64_11858` `sinh-def_binary64_11857` `tan-neg_binary64_11804` `cos-neg_binary64_11803` `sin-neg_binary64_11802` `tan-0_binary64_11801` `cos-0_binary64_11800` `sin-0_binary64_11799` `hang-m-tan_binary64_11798` `hang-p-tan_binary64_11797` `hang-m0-tan_binary64_11796` `hang-p0-tan_binary64_11795` `hang-0m-tan_binary64_11794` `hang-0p-tan_binary64_11793` `tan-+PI/2_binary64_11792` `tan-+PI_binary64_11791` `tan-PI_binary64_11790` `tan-PI/3_binary64_11789` `tan-PI/4_binary64_11788` `tan-PI/6_binary64_11787` `cos-+PI/2_binary64_11786` `cos-+PI_binary64_11785` `cos-PI_binary64_11784` `cos-PI/2_binary64_11783` `cos-PI/3_binary64_11782` `cos-PI/4_binary64_11781` `cos-PI/6_binary64_11780` `sin-+PI/2_binary64_11779` `sin-+PI_binary64_11778` `sin-PI_binary64_11777` `sin-PI/2_binary64_11776` `sin-PI/3_binary64_11775` `sin-PI/4_binary64_11774` `sin-PI/6_binary64_11773` `sub-1-sin_binary64_11772` `sub-1-cos_binary64_11771` `-1-add-sin_binary64_11770` `-1-add-cos_binary64_11769` `1-sub-sin_binary64_11768` `1-sub-cos_binary64_11767` `cos-sin-sum_binary64_11766` `log-E_binary64_11762` `pow-base-0_binary64_11756` `unpow1/3_binary64_11739` `unpow1/2_binary64_11736` `exp-to-pow_binary64_11734` `pow-base-1_binary64_11732` `unpow0_binary64_11731` `unpow-1_binary64_11729` `exp-lft-cube_binary64_11728` `exp-lft-sqr_binary64_11727` `exp-cbrt_binary64_11726` `exp-diff_binary64_11720` `exp-neg_binary64_11719` `exp-sum_binary64_11718` `e-exp-1_binary64_11717` `exp-0_binary64_11714` `rem-exp-log_binary64_11712` `cube-neg_binary64_11699` `rem-3cbrt-rft_binary64_11698` `rem-3cbrt-lft_binary64_11697` `rem-cube-cbrt_binary64_11695` `sqr-abs_binary64_11687` `sqr-neg_binary64_11686` `sub0-neg_binary64_11659` `--rgt-identity_binary64_11658` `+-rgt-identity_binary64_11657` `+-lft-identity_binary64_11656` `mul0-rgt_binary64_11655` `mul0-lft_binary64_11654` `+-inverses_binary64_11651` `lft-mult-inverse_binary64_11650` `rgt-mult-inverse_binary64_11649` `remove-double-div_binary64_11648` `difference-of-sqr--1_binary64_11643` `difference-of-sqr-1_binary64_11642` `distribute-rgt1-in_binary64_11628` `distribute-lft1-in_binary64_11627` `distribute-lft-out--_binary64_11624` `associate--l-_binary64_11610` `associate--l+_binary64_11609` `associate-+l-_binary64_11607` `associate-+r-_binary64_11606`

Counts

188 → 306

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	4252
1	677	3936
2	2878	3783

prune416.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	304	2	306
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	306	8	314

Error

2.0b

Counts

314 → 8

Compiler

Compiled 8003 to 2956 computations (63.1% saved)

regimes2.1s (11.6%)

Accuracy

Total 3.4b remaining (52.9%)

Threshold costs 0b (0%)

Compiler

Compiled 11440 to 9055 computations (20.8% saved)

bsearch86.0ms (0.5%)

Steps

Iters	Range		Point
7	3.0979315438764894e-13	7.969721785309229e-12	7.8352056567318e-12
10	-1.4620706567963576e+68	-1.714069030861187e+58	-2.3321377759488846e+67

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64_11603`
11×	`sub-neg_binary64_11665` `+-commutative_binary64_11602`
8×	`neg-mul-1_binary64_11668` `neg-sub0_binary64_11667`
6×	`distribute-rgt-neg-in_binary64_11630`
4×	`cancel-sign-sub-inv_binary64_11638` `distribute-lft-neg-in_binary64_11629`
2×	`distribute-lft-neg-out_binary64_11631`
1×	`distribute-neg-frac_binary64_11636`
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_11932` `if-if-and_binary64_11931` `if-if-or-not_binary64_11930` `if-if-or_binary64_11929` `if-not_binary64_11928` `if-same_binary64_11927` `if-false_binary64_11926` `if-true_binary64_11925` `tan-0_binary64_11801` `cos-0_binary64_11800` `sin-0_binary64_11799` `unpow1_binary64_11730` `e-exp-1_binary64_11717` `1-exp_binary64_11716` `exp-1-e_binary64_11715` `exp-0_binary64_11714` `sqr-abs_binary64_11687` `sqr-neg_binary64_11686` `unsub-neg_binary64_11666` `mul-1-neg_binary64_11664` `/-rgt-identity_binary64_11663` `-rgt-identity_binary64_11662` `-lft-identity_binary64_11661` `remove-double-neg_binary64_11660` `sub0-neg_binary64_11659` `--rgt-identity_binary64_11658` `+-rgt-identity_binary64_11657` `+-lft-identity_binary64_11656` `cancel-sign-sub_binary64_11637` `distribute-frac-neg_binary64_11635` `distribute-neg-out_binary64_11634` `distribute-neg-in_binary64_11633` `distribute-rgt-neg-out_binary64_11632`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	107
1	59	107
2	80	107
3	99	107
4	111	107
5	115	107
6	116	107

Proof

(if real (<= f64 h0 -23321377759488845731046931249929621261940212508823956325220539695104) (* f64 h1 (/ f64 h2 (/ f64 (- f64 (* f64 1/2 (/ f64 h3 (/ f64 h0 h4))) h0) h0))) (if real (<= f64 h0 4849757399251799/618970019642690137449562112) (* f64 (/ f64 h1 (/ f64 (sqrt f64 (sqrt f64 (- f64 (* f64 h0 h0) (* f64 h3 h4)))) (* f64 (cbrt f64 h0) (cbrt f64 h0)))) (/ f64 h2 (/ f64 (sqrt f64 (sqrt f64 (- f64 (* f64 h0 h0) (* f64 h3 h4)))) (cbrt f64 h0)))) (* f64 h1 (/ f64 h2 (/ f64 (- f64 h0 (* f64 1/2 (=> (* f64 (/ f64 h3 h0) h4)))) h0)))))
*-commutative_binary64_11603 =>
(if real (<= f64 h0 -23321377759488845731046931249929621261940212508823956325220539695104) (* f64 h1 (/ f64 h2 (/ f64 (- f64 (* f64 1/2 (/ f64 h3 (/ f64 h0 h4))) h0) h0))) (if real (<= f64 h0 4849757399251799/618970019642690137449562112) (* f64 (/ f64 h1 (/ f64 (sqrt f64 (sqrt f64 (- f64 (* f64 h0 h0) (* f64 h3 h4)))) (* f64 (cbrt f64 h0) (cbrt f64 h0)))) (/ f64 h2 (/ f64 (sqrt f64 (sqrt f64 (- f64 (* f64 h0 h0) (* f64 h3 h4)))) (cbrt f64 h0)))) (* f64 h1 (/ f64 h2 (/ f64 (- f64 h0 (* f64 1/2 (* f64 h4 (/ f64 h3 h0)))) h0)))))

end0.0ms (0%)

sample2.2s (12%)

Algorithm

1×

intervals

Results

409.0ms	8000×	body	128	valid
98.0ms	2267×	body	128	nan
49.0ms	860×	body	128	invalid

Compiler

Compiled 1333 to 1035 computations (22.4% saved)

Details

analyze1.1s (6.2%)

sample36.0ms (0.2%)

simplify855.0ms (4.7%)

prune14.0ms (0.1%)

localize11.0ms (0.1%)

rewrite211.0ms (1.2%)

series1.4s (7.7%)

simplify508.0ms (2.8%)

prune566.0ms (3.1%)

localize11.0ms (0.1%)

rewrite579.0ms (3.2%)

series1.5s (8.4%)

simplify743.0ms (4.1%)

prune1.0s (5.6%)

localize10.0ms (0.1%)

rewrite126.0ms (0.7%)

series1.7s (9.3%)

simplify414.0ms (2.3%)

prune352.0ms (2%)

localize13.0ms (0.1%)

rewrite180.0ms (1%)

series1.3s (6.9%)

simplify660.0ms (3.7%)

prune416.0ms (2.3%)

regimes2.1s (11.6%)

bsearch86.0ms (0.5%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample2.2s (12%)

Profiling