Details

analyze1.9s (23.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0.8%	98.9%	0.3%	13
1.2%	98.5%	0.3%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample43.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
3.0ms	33×	body	128	invalid

Compiler

Compiled 75 to 67 computations (10.7% saved)

simplify185.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4955	55
1	4955	55

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

32.2b

Counts

2 → 1

Compiler

Compiled 74 to 60 computations (18.9% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
0.1b	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
2.2b	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
31.1b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))

rewrite76.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_11012`
15×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
12×	`add-cube-cbrt_binary64_11025` `*-un-lft-identity_binary64_10990`
10×	`pow1_binary64_11051`
9×	`associate-r_binary64_10930` `associate-l_binary64_10931`
5×	`flip3-+_binary64_10993` `flip-+_binary64_10964`
4×	`prod-exp_binary64_11039` `associate-r/_binary64_10932` `add-log-exp_binary64_11029` `cbrt-unprod_binary64_11023` `associate-l/_binary64_10933`
3×	`times-frac_binary64_10996` `unswap-sqr_binary64_10958` `associate-/r_binary64_10934` `-commutative_binary64_10921` `pow-prod-down_binary64_11061`
2×	`associate-/l/_binary64_10937` `div-exp_binary64_11041` `associate-/r/_binary64_10936` `cbrt-undiv_binary64_11024`
1×	`clear-num_binary64_10989` `associate-/l*_binary64_10935` `distribute-rgt-in_binary64_10940` `frac-2neg_binary64_11001` `div-inv_binary64_10987` `distribute-lft-in_binary64_10939`

Counts

4 → 87

Calls

4 calls:

29.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
18.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
11.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
7.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)

series708.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

481.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
169.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
37.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
20.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5121	3033

prune234.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Error

0.5b

Counts

100 → 7

Compiler

Compiled 4800 to 3220 computations (32.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b

(+.f64 x (+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))))

0.0b

(+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)))

2.0b

(*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_11012`
15×	`*-un-lft-identity_binary64_10990`
13×	`associate-l_binary64_10931`
11×	`add-cube-cbrt_binary64_11025`
10×	`times-frac_binary64_10996` `add-log-exp_binary64_11029`
8×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
5×	`pow1_binary64_11051`
4×	`sum-log_binary64_11081` `associate-r_binary64_10930` `flip3-+_binary64_10993` `flip-+_binary64_10964`
3×	`associate-+r+_binary64_10922`
2×	`prod-exp_binary64_11039` `frac-times_binary64_11000` `associate-*r/_binary64_10932` `distribute-lft-out_binary64_10941` `unswap-sqr_binary64_10958` `+-commutative_binary64_10920` `cbrt-unprod_binary64_11023` `distribute-rgt-in_binary64_10940` `distribute-lft-in_binary64_10939`
1×	`div-exp_binary64_11041` `div-inv_binary64_10987` `-commutative_binary64_10921` `cbrt-undiv_binary64_11024` `associate-l/_binary64_10933` `pow-prod-down_binary64_11061`

Counts

3 → 66

Calls

3 calls:

13.0ms

(*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))

7.0ms

(+.f64 x (+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))))

5.0ms

(+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)))

series156.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

68.0ms

(+.f64 x (+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))))

49.0ms

(*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))

39.0ms

(+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)))

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4961	1553
1	4961	1553

prune91.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	73	9	82

Error

0.2b

Counts

82 → 9

Compiler

Compiled 1955 to 1065 computations (45.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
2.8b	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) (/.f64 (cbrt.f64 y) z)))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-exp-log_binary64_11028`
31×	`prod-exp_binary64_11039` `add-cbrt-cube_binary64_11026`
18×	`cbrt-unprod_binary64_11023`
17×	`div-exp_binary64_11041`
9×	`frac-times_binary64_11000` `pow1_binary64_11051` `add-cube-cbrt_binary64_11025` `cbrt-prod_binary64_11021` `*-un-lft-identity_binary64_10990` `add-sqr-sqrt_binary64_11012` `cbrt-undiv_binary64_11024`
7×	`associate-r/_binary64_10932` `associate-l*_binary64_10931`
6×	`1-exp_binary64_11034`
5×	`associate-*l/_binary64_10933`
4×	`add-log-exp_binary64_11029` `flip3-+_binary64_10993` `flip-+_binary64_10964`
3×	`times-frac_binary64_10996` `pow-prod-down_binary64_11061` `pow1/3_binary64_11072`
1×	`associate-r_binary64_10930` `div-inv_binary64_10987` `*-commutative_binary64_10921`

Counts

4 → 86

Calls

4 calls:

19.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) (/.f64 (cbrt.f64 y) z)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series337.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (*.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) (/.f64 (cbrt.f64 y) z)))
86.0ms	(cbrt.f64 y)
82.0ms	(cbrt.f64 y)
81.0ms	(cbrt.f64 y)

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5045	1165

prune111.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	98	9	107

Error

0.2b

Counts

107 → 9

Compiler

Compiled 2589 to 1369 computations (47.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)
0.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) (/.f64 y (cbrt.f64 z))))
1.9b	(*.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) (/.f64 y (cbrt.f64 z)))

rewrite58.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-exp-log_binary64_11028`
46×	`prod-exp_binary64_11039`
35×	`add-cbrt-cube_binary64_11026`
30×	`add-sqr-sqrt_binary64_11012`
24×	`*-un-lft-identity_binary64_10990`
23×	`times-frac_binary64_10996` `associate-r_binary64_10930`
22×	`add-cube-cbrt_binary64_11025`
20×	`div-exp_binary64_11041` `cbrt-unprod_binary64_11023`
16×	`cbrt-prod_binary64_11021`
11×	`frac-times_binary64_11000` `pow1_binary64_11051` `associate-l_binary64_10931`
10×	`cbrt-undiv_binary64_11024`
8×	`associate-*r/_binary64_10932`
7×	`associate-*l/_binary64_10933`
6×	`1-exp_binary64_11034` `flip3-+_binary64_10993` `flip-+_binary64_10964` `rec-exp_binary64_11040`
4×	`add-log-exp_binary64_11029` `pow-prod-down_binary64_11061`
3×	`unswap-sqr_binary64_10958`
2×	`div-inv_binary64_10987` `*-commutative_binary64_10921` `pow1/3_binary64_11072`
1×	`distribute-lft-out_binary64_10941`

Counts

4 → 128

Calls

4 calls:

25.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) (/.f64 y (cbrt.f64 z))))
17.0ms	(*.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) (/.f64 y (cbrt.f64 z)))
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)

series448.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(*.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) (/.f64 y (cbrt.f64 z)))
91.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) (/.f64 y (cbrt.f64 z))))
83.0ms	(cbrt.f64 z)
83.0ms	(cbrt.f64 z)

simplify116.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4954	2223
1	4954	2223

prune158.0ms (1.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	140	9	149

Error

0.2b

Counts

149 → 9

Compiler

Compiled 3650 to 1796 computations (50.8% saved)

regimes1.2s (15%)

Accuracy

Total 0.7b remaining (69.8%)

Threshold costs 0.7b (69.8%)

Compiler

Compiled 8900 to 7126 computations (19.9% saved)

bsearch79.0ms (1%)

Steps

Iters	Range		Point
8	6.694220852614663e+42	4.039764659862038e+45	2.6725087956259304e+43
10	-3.6342324008015894e+68	-3.026694287976416e+58	-1.5826630768290659e+59

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	126
1	84	126

end0.0ms (0%)

sample1.9s (23.5%)

Algorithm

1×

intervals

Results

711.0ms	8000×	body	128	valid
82.0ms	903×	body	128	invalid

Compiler

Compiled 1294 to 1018 computations (21.3% saved)

Details

analyze1.9s (23.4%)

sample43.0ms (0.5%)

simplify185.0ms (2.2%)

prune4.0ms (0%)

localize28.0ms (0.3%)

rewrite76.0ms (0.9%)

series708.0ms (8.6%)

simplify99.0ms (1.2%)

prune234.0ms (2.8%)

localize10.0ms (0.1%)

rewrite30.0ms (0.4%)

series156.0ms (1.9%)

simplify68.0ms (0.8%)

prune91.0ms (1.1%)

localize17.0ms (0.2%)

rewrite32.0ms (0.4%)

series337.0ms (4.1%)

simplify48.0ms (0.6%)

prune111.0ms (1.3%)

localize15.0ms (0.2%)

rewrite58.0ms (0.7%)

series448.0ms (5.4%)

simplify116.0ms (1.4%)

prune158.0ms (1.9%)

regimes1.2s (15%)

bsearch79.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (23.5%)

Profiling