Details

analyze232.0ms (3.7%)

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)

sample74.0ms (1.2%)

Algorithm

1×

intervals

Results

35.0ms	78×	body	1024	valid
10.0ms	122×	body	128	valid
8.0ms	31×	body	512	valid
7.0ms	8×	body	2048	valid
3.0ms	17×	body	256	valid
1.0ms	10×	body	128	overflowed
1.0ms	2×	body	512	invalid
1.0ms	6×	body	128	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify224.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4933	41
1	4933	41

prune7.0ms (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: 33.1b

Counts

2 → 1

Compiler

Compiled 112 to 96 computations (14.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 1 eps) x)
0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
1.7b	(-.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)))))

rewrite100.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_432`
80×	`frac-times_binary64_433` `exp-neg_binary64_470`
60×	`exp-diff_binary64_471` `neg-sub0_binary64_418`
42×	`associate-*l/_binary64_366`
40×	`associate-*r/_binary64_365`
31×	`flip-+_binary64_397` `add-sqr-sqrt_binary64_445` `flip3--_binary64_427` `flip3-+_binary64_426` `flip--_binary64_398`
24×	`*-un-lft-identity_binary64_423`
23×	`associate-l_binary64_364`
20×	`un-div-inv_binary64_421`
10×	`add-cube-cbrt_binary64_458` `pow1_binary64_484` `add-cbrt-cube_binary64_459`
9×	`associate-r_binary64_363`
8×	`add-exp-log_binary64_461`
6×	`times-frac_binary64_429` `difference-of-squares_binary64_392` `add-log-exp_binary64_462`
3×	`pow-prod-down_binary64_494` `prod-exp_binary64_472` `distribute-lft-out_binary64_374` `*-commutative_binary64_354` `difference-of-sqr-1_binary64_393` `unswap-sqr_binary64_391` `cbrt-unprod_binary64_456`
2×	`distribute-lft-out--_binary64_375` `div-inv_binary64_420`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389`

Counts

4 → 181

Calls

4 calls:

22.0ms	(-.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)))))
18.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
18.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
7.0ms	(*.f64 (+.f64 1 eps) x)

series438.0ms (7%)

Counts

4 → 12

Calls

4 calls:

268.0ms	(-.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)))))
82.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
53.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
35.0ms	(*.f64 (+.f64 1 eps) x)

simplify139.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4965	9375
1	4965	9375

prune1.5s (23.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	191	3	194

Merged error: 0.2b

Counts

194 → 3

Compiler

Compiled 28758 to 23189 computations (19.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
6.6b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_445`
12×	`associate-l_binary64_364`
7×	`add-exp-log_binary64_461` `add-log-exp_binary64_462`
6×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
4×	`add-cbrt-cube_binary64_459` `cube-prod_binary64_451` `unswap-sqr_binary64_391` `unpow-prod-down_binary64_502`
3×	`prod-exp_binary64_472` `associate-r_binary64_363`
2×	`diff-log_binary64_515` `pow1_binary64_484` `sqr-pow_binary64_395`
1×	`associate--l+_binary64_360` `sub-neg_binary64_416` `pow-to-exp_binary64_492` `unpow3_binary64_489` `cancel-sign-sub-inv_binary64_389` `pow-exp_binary64_491` `flip3--_binary64_427` `*-commutative_binary64_354` `difference-of-squares_binary64_392` `cube-mult_binary64_453` `flip--_binary64_398` `sum-log_binary64_514` `cbrt-unprod_binary64_456`

Counts

2 → 46

Calls

2 calls:

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

series94.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

55.0ms	(*.f64 (pow.f64 x 3) 2/3)
39.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5056	681

prune91.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	50	5	55

Merged error: 0.2b

Counts

55 → 5

Compiler

Compiled 1643 to 1284 computations (21.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)) 3)
0.1b	(*.f64 (pow.f64 x 3) 2/3)
2.4b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)) 3))
6.6b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_445`
14×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `cbrt-prod_binary64_454`
12×	`associate-l_binary64_364` `cube-prod_binary64_451` `unpow-prod-down_binary64_502`
10×	`add-exp-log_binary64_461`
9×	`add-log-exp_binary64_462`
7×	`add-cbrt-cube_binary64_459`
5×	`pow1_binary64_484` `difference-of-squares_binary64_392`
4×	`unswap-sqr_binary64_391` `sqr-pow_binary64_395` `cube-div_binary64_452`
3×	`unpow3_binary64_489` `prod-exp_binary64_472` `flip3--_binary64_427` `associate-r_binary64_363` `pow-unpow_binary64_500` `cube-mult_binary64_453` `flip--_binary64_398`
2×	`pow-to-exp_binary64_492` `cbrt-div_binary64_455` `diff-log_binary64_515` `pow-exp_binary64_491`
1×	`associate--l+_binary64_360` `sub-neg_binary64_416` `cancel-sign-sub-inv_binary64_389` `pow1/3_binary64_505` `*-commutative_binary64_354` `rem-cbrt-cube_binary64_447` `pow-pow_binary64_495` `rem-cube-cbrt_binary64_446` `sum-log_binary64_514` `cbrt-unprod_binary64_456`

Counts

4 → 98

Calls

4 calls:

11.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)) 3))
11.0ms	(pow.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)) 3)
10.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
7.0ms	(*.f64 (pow.f64 x 3) 2/3)

series161.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(*.f64 (pow.f64 x 3) 2/3)
36.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)) 3))
36.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
34.0ms	(pow.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)) 3)

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4951	2161
1	4951	2161

prune223.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	111	4	115

Merged error: 0.2b

Counts

115 → 4

Compiler

Compiled 3916 to 3140 computations (19.8% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (.f64 x x) (-.f64 (*.f64 x 8) 12))
10.6b	(cbrt.f64 (+.f64 8 (.f64 (.f64 x x) (-.f64 (*.f64 x 8) 12))))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_445` `pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
6×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `cancel-sign-sub-inv_binary64_389`
4×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372`
3×	`pow-prod-down_binary64_494` `prod-exp_binary64_472` `associate-r_binary64_363` `cbrt-prod_binary64_454` `cbrt-unprod_binary64_456`
2×	`sub-neg_binary64_416` `cbrt-div_binary64_455` `associate-*r/_binary64_365` `add-log-exp_binary64_462`
1×	`associate-l_binary64_364` `flip-+_binary64_397` `pow1/3_binary64_505` `flip3--_binary64_427` `*-commutative_binary64_354` `flip3-+_binary64_426` `flip--_binary64_398` `unswap-sqr_binary64_391`

Counts

2 → 42

Calls

2 calls:

12.0ms	(.f64 (.f64 x x) (-.f64 (*.f64 x 8) 12))
3.0ms	(cbrt.f64 (+.f64 8 (.f64 (.f64 x x) (-.f64 (*.f64 x 8) 12))))

series179.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

103.0ms	(.f64 (.f64 x x) (-.f64 (*.f64 x 8) 12))
76.0ms	(cbrt.f64 (+.f64 8 (.f64 (.f64 x x) (-.f64 (*.f64 x 8) 12))))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5196	946

prune67.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	46	6	52

Merged error: 0.2b

Counts

52 → 6

Compiler

Compiled 1353 to 1050 computations (22.4% saved)

regimes104.0ms (1.7%)

Compiler: Compiled 928 to 784 computations (15.5% saved)

bsearch87.0ms (1.4%)

Steps

Iters	Range		Point
10	0.0018529532680710897	3391775993748.8833	12.271515233532067

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	185	68
1	185	68

end0.0ms (0%)

sample2.2s (35.7%)

Algorithm

1×

intervals

Results

893.0ms	2044×	body	1024	valid
347.0ms	4227×	body	128	valid
259.0ms	1032×	body	512	valid
175.0ms	224×	body	2048	valid
75.0ms	473×	body	256	valid
21.0ms	219×	body	128	invalid
14.0ms	179×	body	128	overflowed
8.0ms	15×	body	1024	invalid
4.0ms	15×	body	512	invalid
2.0ms	8×	body	256	invalid

Compiler

Compiled 278 to 235 computations (15.5% saved)

Details

analyze232.0ms (3.7%)

sample74.0ms (1.2%)

simplify224.0ms (3.6%)

prune7.0ms (0.1%)

localize17.0ms (0.3%)

rewrite100.0ms (1.6%)

series438.0ms (7%)

simplify139.0ms (2.2%)

prune1.5s (23.4%)

localize8.0ms (0.1%)

rewrite20.0ms (0.3%)

series94.0ms (1.5%)

simplify52.0ms (0.8%)

prune91.0ms (1.5%)

localize11.0ms (0.2%)

rewrite47.0ms (0.8%)

series161.0ms (2.6%)

simplify84.0ms (1.4%)

prune223.0ms (3.6%)

localize9.0ms (0.1%)

rewrite18.0ms (0.3%)

series179.0ms (2.9%)

simplify63.0ms (1%)

prune67.0ms (1.1%)

regimes104.0ms (1.7%)

bsearch87.0ms (1.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.2s (35.7%)

Profiling