Details

analyze275.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
31.2%	68.6%	0.1%	6
43.7%	56.2%	0.1%	7
59.3%	40.6%	0.1%	8
59.3%	40.6%	0.1%	9
68.6%	31.2%	0.1%	10
78%	21.8%	0.1%	11
78%	21.8%	0.1%	12
83.5%	16.4%	0.1%	13
88.5%	11.3%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	189×	body	128	valid
11.0ms	43×	body	1024	valid
4.0ms	21×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify106.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	227	14
1	227	14

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 z (sin.f64 y))
0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
0.1b	(*.f64 z (sin.f64 y))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_3186`
6×	`add-sqr-sqrt_binary64_3169`
4×	`*-un-lft-identity_binary64_3147` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208` `add-cube-cbrt_binary64_3182`
3×	`associate-r_binary64_3087` `associate-l_binary64_3088`
2×	`diff-log_binary64_3239`
1×	`*-commutative_binary64_3078` `flip--_binary64_3122` `unswap-sqr_binary64_3115` `cancel-sign-sub-inv_binary64_3113` `pow-prod-down_binary64_3218` `associate--l+_binary64_3084` `flip3--_binary64_3151` `sub-neg_binary64_3140` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `sum-log_binary64_3238`

Counts

2 → 32

Calls

4 calls:

9.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
5.0ms	(*.f64 z (sin.f64 y))
0.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
0.0ms	(*.f64 z (sin.f64 y))

series256.0ms (4%)

Counts

2 → 25

Calls

2 calls:

184.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
71.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 351 to 321 computations (8.5% saved)

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5383	700

prune60.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	6	58

Error

Counts

58 → 6

Compiler

Compiled 750 to 183 computations (75.6% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 z (sin.f64 y))
0.0b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
8.4b	(cbrt.f64 (*.f64 z (sin.f64 y)))
8.4b	(cbrt.f64 (*.f64 z (sin.f64 y)))
8.4b	(cbrt.f64 (*.f64 z (sin.f64 y)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_3208`
10×	`add-sqr-sqrt_binary64_3169`
9×	`pow1/3_binary64_3229`
8×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
7×	`cbrt-prod_binary64_3178`
6×	`add-exp-log_binary64_3185`
4×	`add-cbrt-cube_binary64_3183` `swap-sqr_binary64_3114` `associate-r_binary64_3087` `add-log-exp_binary64_3186` `associate-l_binary64_3088`
2×	`pow-prod-down_binary64_3218` `pow-prod-up_binary64_3217` `pow-sqr_binary64_3120`
1×	`*-commutative_binary64_3078` `unswap-sqr_binary64_3115` `prod-exp_binary64_3196` `pow-plus_binary64_3210` `pow2_binary64_3228` `cbrt-unprod_binary64_3180`

Counts

4 → 58

Calls

8 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
3.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))
3.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))
3.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))
0.0ms	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

series918.0ms (14.4%)

Counts

4 → 25

Calls

4 calls:

314.0ms	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
204.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))
203.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))
197.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))

Compiler

Compiled 1353 to 944 computations (30.2% saved)

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4936	821
1	4936	821

prune72.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	83	6	89

Error

Counts

89 → 6

Compiler

Compiled 1977 to 370 computations (81.3% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

31.1b	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
0.2b	(pow.f64 (*.f64 z (sin.f64 y)) 3)
0.1b	(*.f64 z (sin.f64 y))
0.0b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
0.0b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
0.1b	(*.f64 z (sin.f64 y))
0.2b	(pow.f64 (*.f64 z (sin.f64 y)) 3)
31.1b	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64_3178`
17×	`add-sqr-sqrt_binary64_3169`
15×	`*-un-lft-identity_binary64_3147`
11×	`cancel-sign-sub-inv_binary64_3113`
10×	`add-cube-cbrt_binary64_3182`
9×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208` `add-log-exp_binary64_3186`
4×	`sqr-pow_binary64_3119`
3×	`unpow-prod-down_binary64_3226` `associate-r_binary64_3087` `cube-prod_binary64_3175` `difference-of-squares_binary64_3116` `cube-mult_binary64_3177` `pow-unpow_binary64_3224` `associate-l_binary64_3088` `unpow3_binary64_3213`
2×	`pow-exp_binary64_3215` `pow-prod-down_binary64_3218` `rem-cube-cbrt_binary64_3170` `distribute-lft-out--_binary64_3099` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `diff-log_binary64_3239` `pow-pow_binary64_3219`
1×	`rem-cbrt-cube_binary64_3171` `*-commutative_binary64_3078` `flip--_binary64_3122` `unswap-sqr_binary64_3115` `pow1/3_binary64_3229` `associate--l+_binary64_3084` `flip3--_binary64_3151` `pow-to-exp_binary64_3216` `sub-neg_binary64_3140` `distribute-lft-out_binary64_3098` `sum-log_binary64_3238`

Counts

4 → 86

Calls

8 calls:

12.0ms	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
5.0ms	(*.f64 z (sin.f64 y))
5.0ms	(pow.f64 (*.f64 z (sin.f64 y)) 3)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
0.0ms	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

series464.0ms (7.3%)

Counts

4 → 38

Calls

4 calls:

208.0ms	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
127.0ms	(pow.f64 (*.f64 z (sin.f64 y)) 3)
69.0ms	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))
59.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 727 to 664 computations (8.7% saved)

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4964	1489
1	4964	1489

prune83.0ms (1.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	124	6	130

Error

Counts

130 → 6

Compiler

Compiled 1769 to 543 computations (69.3% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
0.0b	(sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
0.0b	(sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 z (sin.f64 y))
0.2b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))

rewrite49.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_3169`
24×	`pow1_binary64_3208`
21×	`sqrt-prod_binary64_3163`
17×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
14×	`sqrt-div_binary64_3164`
12×	`associate-r_binary64_3087` `associate-l_binary64_3088`
10×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
9×	`sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
8×	`swap-sqr_binary64_3114`
7×	`flip--_binary64_3122` `flip3--_binary64_3151`
6×	`unswap-sqr_binary64_3115`
5×	`pow-prod-down_binary64_3218` `pow-prod-up_binary64_3217`
4×	`frac-times_binary64_3157` `add-log-exp_binary64_3186`
3×	`*-commutative_binary64_3078` `rem-sqrt-square_binary64_3160` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `pow-sqr_binary64_3120`
2×	`associate-l/_binary64_3090` `associate-r/_binary64_3089`
1×	`sqrt-unprod_binary64_3167` `sqr-abs_binary64_3162` `pow-plus_binary64_3210` `pow2_binary64_3228` `rem-square-sqrt_binary64_3159`

Counts

4 → 109

Calls

8 calls:

19.0ms	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
7.0ms	(sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
6.0ms	(*.f64 z (sin.f64 y))
5.0ms	(*.f64 z (sin.f64 y))
0.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

series519.0ms (8.1%)

Counts

4 → 50

Calls

4 calls:

200.0ms	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
191.0ms	(sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
66.0ms	(*.f64 z (sin.f64 y))
63.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 1649 to 1097 computations (33.5% saved)

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5021	3009

prune123.0ms (1.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	159	6	165

Error

Counts

165 → 6

Compiler

Compiled 3743 to 657 computations (82.4% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	331	345
1	331	345

regimes136.0ms (2.1%)

Compiler: Compiled 904 to 742 computations (17.9% saved)

bsearch0.0ms (0%)

regimes130.0ms (2%)

Compiler: Compiled 153 to 204 computations (-33.3% saved)

bsearch38.0ms (0.6%)

Steps

Iters	Range		Point
6	2.0128805823676512e-32	1.2052883521833036e-31	1.1853413812390224e-31
6	-4.765692224742377e+53	-4.5552852994556143e+52	-4.617795998451085e+52

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes117.0ms (1.8%)

Compiler: Compiled 132 to 183 computations (-38.6% saved)

bsearch102.0ms (1.6%)

Steps

Iters	Range		Point
9	4.030358090158805e+26	7.44513213506171e+31	4.295310622478322e+26
4	-5.241619999368039	-3.6186604588671747	-5.053716960464881
5	-1.9742353685525258e+25	-5.67315228043989e+24	-6.929473909826237e+24
6	-2.53708577891696e+88	-5.841609548996868e+87	-2.4577894350339715e+88
9	-2.314816404388014e+138	-2.633931214481134e+132	-1.518515463397373e+133

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes126.0ms (2%)

Compiler: Compiled 108 to 162 computations (-50% saved)

bsearch120.0ms (1.9%)

Steps

Iters	Range		Point
7	1.2174788082581859e-15	7.8002142219098e-14	7.6669548423569e-14
9	-0.00031753722337157916	-1.2081174785856992e-10	-0.0003124677607253619
4	-5.241619999368039	-3.6186604588671747	-5.178985653066986
5	-1.9742353685525258e+25	-5.67315228043989e+24	-5.812743572593929e+24
6	-2.53708577891696e+88	-5.841609548996868e+87	-2.5106536642892974e+88
9	-2.314816404388014e+138	-2.633931214481134e+132	-2.6612415537441975e+132

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes70.0ms (1.1%)

Compiler: Compiled 93 to 144 computations (-54.8% saved)

bsearch43.0ms (0.7%)

Steps

Iters	Range		Point
7	1.2174788082581859e-15	7.8002142219098e-14	7.6669548423569e-14
9	-0.00031753722337157916	-1.2081174785856992e-10	-0.0002719120595556238

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes73.0ms (1.1%)

Compiler: Compiled 81 to 129 computations (-59.3% saved)

bsearch42.0ms (0.7%)

Steps

Iters	Range		Point
9	4.030358090158805e+26	7.44513213506171e+31	4.083348596622708e+26
6	-7.831564401552817e+30	-1.5946017445408774e+30	-1.753118415588741e+30

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes66.0ms (1%)

Compiler: Compiled 48 to 99 computations (-106.3% saved)

bsearch33.0ms (0.5%)

Steps

Iters	Range		Point
9	4.030358090158805e+26	7.44513213506171e+31	8.531729774650604e+29
4	-5.241619999368039	-3.6186604588671747	-3.649977632017701

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes33.0ms (0.5%)

Compiler: Compiled 27 to 78 computations (-188.9% saved)

bsearch0.0ms (0%)

regimes98.0ms (1.5%)

Compiler: Compiled 18 to 63 computations (-250% saved)

bsearch63.0ms (1%)

Steps

Iters	Range		Point
9	0.0002105607146670681	500.57286289967595	1.0194997779622874
8	-1.5031532792867232e-21	-3.370730535796665e-24	-1.4886679085051663e-21

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes27.0ms (0.4%)

Accuracy

Total 0.0b remaining (62.5%)

Threshold costs 0.0b (62.5%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch11.0ms (0.2%)

Compiler: Compiled 220 to 148 computations (32.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	183	314
1	183	314

end0.0ms (0%)

sample1.7s (26.2%)

Algorithm

1×

intervals

Results

371.0ms	5733×	body	128	valid
355.0ms	1314×	body	1024	valid
127.0ms	656×	body	512	valid
45.0ms	296×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 440 to 337 computations (23.4% saved)

Pareto

0.5110286837537678

Details

analyze275.0ms (4.3%)

sample42.0ms (0.7%)

simplify106.0ms (1.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite16.0ms (0.3%)

series256.0ms (4%)

simplify70.0ms (1.1%)

prune60.0ms (0.9%)

localize15.0ms (0.2%)

rewrite22.0ms (0.3%)

series918.0ms (14.4%)

simplify63.0ms (1%)

prune72.0ms (1.1%)

localize14.0ms (0.2%)

rewrite30.0ms (0.5%)

series464.0ms (7.3%)

simplify71.0ms (1.1%)

prune83.0ms (1.3%)

localize13.0ms (0.2%)

rewrite49.0ms (0.8%)

series519.0ms (8.1%)

simplify77.0ms (1.2%)

prune123.0ms (1.9%)

simplify10.0ms (0.2%)

regimes136.0ms (2.1%)

bsearch0.0ms (0%)

regimes130.0ms (2%)

bsearch38.0ms (0.6%)

regimes117.0ms (1.8%)

bsearch102.0ms (1.6%)

regimes126.0ms (2%)

bsearch120.0ms (1.9%)

regimes70.0ms (1.1%)

bsearch43.0ms (0.7%)

regimes73.0ms (1.1%)

bsearch42.0ms (0.7%)

regimes66.0ms (1%)

bsearch33.0ms (0.5%)

regimes33.0ms (0.5%)

bsearch0.0ms (0%)

regimes98.0ms (1.5%)

bsearch63.0ms (1%)

regimes27.0ms (0.4%)

bsearch11.0ms (0.2%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample1.7s (26.2%)

Profiling