Details

analyze222.0ms (3.5%)

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
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample63.0ms (1%)

Algorithm

1×

intervals

Results

23.0ms	56×	body	1024	valid
11.0ms	37×	body	512	valid
11.0ms	136×	body	128	valid
4.0ms	5×	body	2048	valid
4.0ms	22×	body	256	valid
1.0ms	8×	body	128	invalid
0.0ms	3×	body	128	overflowed

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify157.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5212	41

prune4.0ms (0.1%)

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

Merged error: 29.9b

Counts

2 → 1

Compiler

Compiled 56 to 48 computations (14.3% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
2.7b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite66.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_428`
78×	`exp-neg_binary64_466`
76×	`frac-times_binary64_429`
59×	`exp-diff_binary64_467` `neg-sub0_binary64_414`
38×	`associate-l/_binary64_362` `associate-r/_binary64_361`
30×	`flip3-+_binary64_422` `flip-+_binary64_393`
28×	`flip3--_binary64_423` `flip--_binary64_394`
19×	`un-div-inv_binary64_417`
12×	`exp-prod_binary64_471`
11×	`*-un-lft-identity_binary64_419`
10×	`add-log-exp_binary64_458` `add-sqr-sqrt_binary64_441`
8×	`add-cube-cbrt_binary64_454`
6×	`add-cbrt-cube_binary64_455` `pow1_binary64_480`
5×	`associate-l_binary64_360` `add-exp-log_binary64_457`
4×	`rem-exp-log_binary64_459`
3×	`associate-r_binary64_359`
2×	`distribute-lft-neg-in_binary64_376` `neg-mul-1_binary64_415` `distribute-rgt-neg-in_binary64_377` `distribute-lft-out_binary64_370` `neg-log_binary64_512`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `div-inv_binary64_416` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 156

Calls

4 calls:

20.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
13.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

series201.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
28.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
20.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
17.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4985	8651
1	4985	8651

prune508.0ms (8.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	163	5	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	5	169

Merged error: 0.6b

Counts

169 → 5

Compiler

Compiled 7948 to 6137 computations (22.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 3))
6.0b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_441`
12×	`associate-r_binary64_359`
7×	`add-log-exp_binary64_458` `add-exp-log_binary64_457`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
4×	`unpow-prod-down_binary64_498` `unswap-sqr_binary64_387` `cube-prod_binary64_447` `add-cbrt-cube_binary64_455`
3×	`prod-exp_binary64_468` `associate-l_binary64_360`
2×	`sqr-pow_binary64_391` `diff-log_binary64_511` `pow1_binary64_480`
1×	`associate--l+_binary64_356` `sub-neg_binary64_412` `difference-of-squares_binary64_388` `unpow3_binary64_485` `cube-mult_binary64_449` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `sum-log_binary64_510` `flip3--_binary64_423` `pow-to-exp_binary64_488` `*-commutative_binary64_350` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`

Counts

2 → 46

Calls

2 calls:

9.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
7.0ms	(*.f64 2/3 (pow.f64 x 3))

series42.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

25.0ms	(*.f64 2/3 (pow.f64 x 3))
18.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4912	670
1	4912	670

prune63.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 0.6b

Counts

57 → 7

Compiler

Compiled 1119 to 839 computations (25% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.0b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 2/3 (pow.f64 x 3))) (cbrt.f64 (.f64 2/3 (pow.f64 x 3)))) (cbrt.f64 (.f64 2/3 (pow.f64 x 3)))) 2) (.f64 x x))
41.6b	(cbrt.f64 (*.f64 2/3 (pow.f64 x 3)))
41.6b	(cbrt.f64 (*.f64 2/3 (pow.f64 x 3)))
41.6b	(cbrt.f64 (*.f64 2/3 (pow.f64 x 3)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64_458`
5×	`add-sqr-sqrt_binary64_441`
4×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`pow1/3_binary64_501` `cbrt-prod_binary64_450`
2×	`diff-log_binary64_511`
1×	`associate--l+_binary64_356` `sub-neg_binary64_412` `difference-of-squares_binary64_388` `sum-log_binary64_510` `flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 42

Calls

4 calls:

13.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 2/3 (pow.f64 x 3))) (cbrt.f64 (.f64 2/3 (pow.f64 x 3)))) (cbrt.f64 (.f64 2/3 (pow.f64 x 3)))) 2) (.f64 x x))
4.0ms	(cbrt.f64 (*.f64 2/3 (pow.f64 x 3)))
4.0ms	(cbrt.f64 (*.f64 2/3 (pow.f64 x 3)))
3.0ms	(cbrt.f64 (*.f64 2/3 (pow.f64 x 3)))

series103.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 2/3 (pow.f64 x 3))) (cbrt.f64 (.f64 2/3 (pow.f64 x 3)))) (cbrt.f64 (.f64 2/3 (pow.f64 x 3)))) 2) (.f64 x x))
22.0ms	(cbrt.f64 (*.f64 2/3 (pow.f64 x 3)))
22.0ms	(cbrt.f64 (*.f64 2/3 (pow.f64 x 3)))
22.0ms	(cbrt.f64 (*.f64 2/3 (pow.f64 x 3)))

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4939	707
1	4939	707

prune90.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Merged error: 0.6b

Counts

61 → 7

Compiler

Compiled 1689 to 1339 computations (20.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3)
0.1b	(*.f64 2/3 (pow.f64 x 3))
2.8b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3))
6.0b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `cbrt-prod_binary64_450`
12×	`unpow-prod-down_binary64_498` `associate-r_binary64_359` `cube-prod_binary64_447`
10×	`add-exp-log_binary64_457`
9×	`add-log-exp_binary64_458`
7×	`add-cbrt-cube_binary64_455`
5×	`difference-of-squares_binary64_388` `pow1_binary64_480`
4×	`unswap-sqr_binary64_387` `sqr-pow_binary64_391` `cube-div_binary64_448`
3×	`unpow3_binary64_485` `cube-mult_binary64_449` `prod-exp_binary64_468` `flip3--_binary64_423` `associate-l_binary64_360` `pow-unpow_binary64_496` `flip--_binary64_394`
2×	`cbrt-div_binary64_451` `pow-exp_binary64_487` `pow-to-exp_binary64_488` `diff-log_binary64_511`
1×	`pow1/3_binary64_501` `associate--l+_binary64_356` `sub-neg_binary64_412` `rem-cube-cbrt_binary64_442` `cbrt-unprod_binary64_452` `sum-log_binary64_510` `rem-cbrt-cube_binary64_443` `*-commutative_binary64_350` `pow-pow_binary64_491` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 98

Calls

4 calls:

9.0ms	(pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3)
9.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3))
9.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
7.0ms	(*.f64 2/3 (pow.f64 x 3))

series78.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(*.f64 2/3 (pow.f64 x 3))
19.0ms	(pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3)
18.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3))
18.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5080	2168

prune134.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	4	5
Picked	1	0	1
Done	1	0	1
Total	112	5	117

Merged error: 0.6b

Counts

117 → 5

Compiler

Compiled 2434 to 1836 computations (24.6% saved)

regimes591.0ms (9.4%)

Compiler: Compiled 8032 to 6712 computations (16.4% saved)

bsearch79.0ms (1.2%)

Steps

Iters	Range		Point
9	2.780941951221814	196769096.11102018	670.6727462917139

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	72
1	61	72

end0.0ms (0%)

sample3.5s (54.9%)

Algorithm

1×

intervals

Results

840.0ms	2017×	body	1024	valid
347.0ms	4263×	body	128	valid
258.0ms	1020×	body	512	valid
142.0ms	204×	body	2048	valid
80.0ms	496×	body	256	valid
18.0ms	214×	body	128	invalid
15.0ms	194×	body	128	overflowed
8.0ms	19×	body	1024	invalid
3.0ms	9×	body	512	invalid
2.0ms	12×	body	256	invalid

Compiler

Compiled 2056 to 1719 computations (16.4% saved)

Details

analyze222.0ms (3.5%)

sample63.0ms (1%)

simplify157.0ms (2.5%)

prune4.0ms (0.1%)

localize20.0ms (0.3%)

rewrite66.0ms (1.1%)

series201.0ms (3.2%)

simplify125.0ms (2%)

prune508.0ms (8.1%)

localize7.0ms (0.1%)

rewrite18.0ms (0.3%)

series42.0ms (0.7%)

simplify61.0ms (1%)

prune63.0ms (1%)

localize13.0ms (0.2%)

rewrite27.0ms (0.4%)

series103.0ms (1.6%)

simplify40.0ms (0.6%)

prune90.0ms (1.4%)

localize10.0ms (0.2%)

rewrite45.0ms (0.7%)

series78.0ms (1.2%)

simplify67.0ms (1.1%)

prune134.0ms (2.1%)

regimes591.0ms (9.4%)

bsearch79.0ms (1.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (54.9%)

Profiling