Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.8%	0.1%	0.1%	12
99.8%	0%	0.1%	13
99.8%	0%	0.2%	14

Compiler

Compiled 10 to 10 computations (0% saved)

sample13.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify97.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7

prune4.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 10 to 10 computations (0% saved)

localize4.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 841/108 x)
0.0b	(+.f64 (*.f64 841/108 x) 4/29)
0.0b	(+.f64 (*.f64 841/108 x) 4/29)
0.2b	(*.f64 841/108 x)

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_8966`
4×	`add-cube-cbrt_binary64_8979` `*-un-lft-identity_binary64_8944` `pow1_binary64_9005` `add-cbrt-cube_binary64_8980` `add-log-exp_binary64_8983` `add-exp-log_binary64_8982`
3×	`associate-l_binary64_8885` `associate-r_binary64_8884`
1×	`flip3-+_binary64_8947` `+-commutative_binary64_8874` `prod-exp_binary64_8993` `*-commutative_binary64_8875` `sum-log_binary64_9035` `unswap-sqr_binary64_8912` `pow-prod-down_binary64_9015` `flip-+_binary64_8918` `cbrt-unprod_binary64_8977`

Counts

2 → 29

Calls

4 calls:

7.0ms	(+.f64 (*.f64 841/108 x) 4/29)
4.0ms	(*.f64 841/108 x)
0.0ms	(+.f64 (*.f64 841/108 x) 4/29)
0.0ms	(*.f64 841/108 x)

series43.0ms (2.1%)

Counts

2 → 9

Calls

2 calls:

26.0ms	(+.f64 (*.f64 841/108 x) 4/29)
16.0ms	(*.f64 841/108 x)

Compiler

Compiled 67 to 68 computations (-1.5% saved)

simplify76.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5087	284

prune44.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Error

Counts

39 → 4

Compiler

Compiled 334 to 279 computations (16.5% saved)

localize6.0ms (0.3%)

Local error

Found 6 expressions with local error:

0.3b	(.f64 (sqrt.f64 841/108) (.f64 x (sqrt.f64 841/108)))
0.2b	(*.f64 x (sqrt.f64 841/108))
0.0b	(+.f64 (.f64 (sqrt.f64 841/108) (.f64 x (sqrt.f64 841/108))) 4/29)
0.0b	(+.f64 (.f64 (sqrt.f64 841/108) (.f64 x (sqrt.f64 841/108))) 4/29)
0.2b	(*.f64 x (sqrt.f64 841/108))
0.3b	(.f64 (sqrt.f64 841/108) (.f64 x (sqrt.f64 841/108)))

rewrite24.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_8966`
10×	`pow1_binary64_9005` `add-cbrt-cube_binary64_8980` `add-exp-log_binary64_8982`
9×	`associate-l_binary64_8885`
8×	`add-cube-cbrt_binary64_8979` `*-un-lft-identity_binary64_8944`
7×	`associate-r_binary64_8884` `sqrt-prod_binary64_8960`
5×	`add-log-exp_binary64_8983`
4×	`prod-exp_binary64_8993` `pow-prod-down_binary64_9015` `cbrt-unprod_binary64_8977`
2×	`*-commutative_binary64_8875` `unswap-sqr_binary64_8912`
1×	`flip3-+_binary64_8947` `+-commutative_binary64_8874` `sum-log_binary64_9035` `flip-+_binary64_8918`

Counts

3 → 54

Calls

6 calls:

8.0ms	(+.f64 (.f64 (sqrt.f64 841/108) (.f64 x (sqrt.f64 841/108))) 4/29)
7.0ms	(.f64 (sqrt.f64 841/108) (.f64 x (sqrt.f64 841/108)))
5.0ms	(*.f64 x (sqrt.f64 841/108))
0.0ms	(+.f64 (.f64 (sqrt.f64 841/108) (.f64 x (sqrt.f64 841/108))) 4/29)
0.0ms	(*.f64 x (sqrt.f64 841/108))

series139.0ms (6.9%)

Counts

3 → 12

Calls

3 calls:

58.0ms	(+.f64 (.f64 (sqrt.f64 841/108) (.f64 x (sqrt.f64 841/108))) 4/29)
47.0ms	(.f64 (sqrt.f64 841/108) (.f64 x (sqrt.f64 841/108)))
34.0ms	(*.f64 x (sqrt.f64 841/108))

Compiler

Compiled 163 to 164 computations (-0.6% saved)

simplify49.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4946	520
1	4946	520

prune51.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	66	4	70

Error

Counts

70 → 4

Compiler

Compiled 705 to 616 computations (12.6% saved)

localize7.0ms (0.4%)

Local error

Found 8 expressions with local error:

1.0b	(*.f64 (cbrt.f64 841/108) (cbrt.f64 841/108))
0.4b	(.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 x (cbrt.f64 841/108)))
0.1b	(*.f64 x (cbrt.f64 841/108))
0.0b	(+.f64 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 x (cbrt.f64 841/108))) 4/29)
0.0b	(+.f64 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 x (cbrt.f64 841/108))) 4/29)
0.1b	(*.f64 x (cbrt.f64 841/108))
0.4b	(.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 x (cbrt.f64 841/108)))
1.0b	(*.f64 (cbrt.f64 841/108) (cbrt.f64 841/108))

rewrite41.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_8966`
25×	`pow1_binary64_9005`
20×	`cbrt-prod_binary64_8975` `add-exp-log_binary64_8982`
15×	`add-cube-cbrt_binary64_8979` `*-un-lft-identity_binary64_8944`
13×	`associate-r_binary64_8884`
11×	`add-cbrt-cube_binary64_8980` `pow-prod-down_binary64_9015`
10×	`associate-l_binary64_8885` `prod-exp_binary64_8993` `cbrt-unprod_binary64_8977`
6×	`pow1/3_binary64_9026` `swap-sqr_binary64_8911` `unswap-sqr_binary64_8912` `add-log-exp_binary64_8983`
3×	`*-commutative_binary64_8875`
2×	`pow-sqr_binary64_8917` `pow-prod-up_binary64_9014`
1×	`flip3-+_binary64_8947` `pow2_binary64_9025` `+-commutative_binary64_8874` `sum-log_binary64_9035` `pow-plus_binary64_9007` `flip-+_binary64_8918`

Counts

4 → 95

Calls

8 calls:

10.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 x (cbrt.f64 841/108))) 4/29)
9.0ms	(.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 x (cbrt.f64 841/108)))
6.0ms	(*.f64 (cbrt.f64 841/108) (cbrt.f64 841/108))
5.0ms	(*.f64 x (cbrt.f64 841/108))
0.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 x (cbrt.f64 841/108))) 4/29)

series166.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 x (cbrt.f64 841/108))) 4/29)
61.0ms	(.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 x (cbrt.f64 841/108)))
33.0ms	(*.f64 x (cbrt.f64 841/108))
0.0ms	(*.f64 (cbrt.f64 841/108) (cbrt.f64 841/108))

Compiler

Compiled 181 to 182 computations (-0.6% saved)

simplify55.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4876	849
1	4876	849

prune104.0ms (5.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	107	4	111

Error

Counts

111 → 4

Compiler

Compiled 1365 to 1235 computations (9.5% saved)

localize7.0ms (0.3%)

Local error

Found 8 expressions with local error:

23.0b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 841/108 x) 4/29) 3))
0.2b	(*.f64 841/108 x)
0.1b	(pow.f64 (+.f64 (*.f64 841/108 x) 4/29) 3)
0.0b	(+.f64 (*.f64 841/108 x) 4/29)
0.0b	(+.f64 (*.f64 841/108 x) 4/29)
0.1b	(pow.f64 (+.f64 (*.f64 841/108 x) 4/29) 3)
0.2b	(*.f64 841/108 x)
23.0b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 841/108 x) 4/29) 3))

rewrite23.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_8966`
12×	`add-cube-cbrt_binary64_8979` `*-un-lft-identity_binary64_8944` `cbrt-prod_binary64_8975`
7×	`pow1_binary64_9005` `add-cbrt-cube_binary64_8980` `add-exp-log_binary64_8982`
6×	`cube-prod_binary64_8972` `unpow-prod-down_binary64_9023` `add-log-exp_binary64_8983`
4×	`cube-div_binary64_8973`
3×	`flip3-+_binary64_8947` `associate-l_binary64_8885` `associate-r_binary64_8884` `pow-unpow_binary64_9021` `flip-+_binary64_8918`
2×	`sqr-pow_binary64_8916` `cbrt-div_binary64_8976` `cube-mult_binary64_8974` `unpow3_binary64_9010`
1×	`rem-cube-cbrt_binary64_8967` `pow1/3_binary64_9026` `+-commutative_binary64_8874` `prod-exp_binary64_8993` `rem-cbrt-cube_binary64_8968` `pow-pow_binary64_9016` `pow-to-exp_binary64_9013` `*-commutative_binary64_8875` `pow-exp_binary64_9012` `sum-log_binary64_9035` `unswap-sqr_binary64_8912` `pow-prod-down_binary64_9015` `cbrt-unprod_binary64_8977`

Counts

4 → 77

Calls

8 calls:

5.0ms	(cbrt.f64 (pow.f64 (+.f64 (*.f64 841/108 x) 4/29) 3))
5.0ms	(pow.f64 (+.f64 (*.f64 841/108 x) 4/29) 3)
4.0ms	(*.f64 841/108 x)
4.0ms	(+.f64 (*.f64 841/108 x) 4/29)
0.0ms	(+.f64 (*.f64 841/108 x) 4/29)

series111.0ms (5.5%)

Counts

4 → 27

Calls

4 calls:

34.0ms	(+.f64 (*.f64 841/108 x) 4/29)
32.0ms	(pow.f64 (+.f64 (*.f64 841/108 x) 4/29) 3)
27.0ms	(cbrt.f64 (pow.f64 (+.f64 (*.f64 841/108 x) 4/29) 3))
17.0ms	(*.f64 841/108 x)

Compiler

Compiled 291 to 281 computations (3.4% saved)

simplify64.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4906	1104
1	4906	1104

prune79.0ms (3.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	104	4	108

Error

Counts

108 → 4

Compiler

Compiled 1149 to 985 computations (14.3% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	124	310
1	124	310

regimes33.0ms (1.7%)

Compiler: Compiled 205 to 192 computations (6.3% saved)

bsearch0.0ms (0%)

regimes23.0ms (1.1%)

Compiler: Compiled 9 to 13 computations (-44.4% saved)

bsearch27.0ms (1.3%)

Steps

Iters	Range		Point
10	8.563846972629209e-15	0.46041642693548235	0.017810429117498975
10	-0.12208613939130855	-6.458788025558041e-18	-0.017613985957795644

Compiler

Compiled 1 to 1 computations (0% saved)

regimes10.0ms (0.5%)

Compiler: Compiled 6 to 10 computations (-66.7% saved)

bsearch0.0ms (0%)

regimes8.0ms (0.4%)

Accuracy

Total 0.1b remaining (98%)

Threshold costs 0.1b (98%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 22 to 21 computations (4.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	28
1	20	28

end0.0ms (0%)

sample685.0ms (33.9%)

Algorithm

1×

intervals

Results

227.0ms	7998×	body	128	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 233 to 221 computations (5.2% saved)

Pareto

0.42865446393179024

Details

analyze4.0ms (0.2%)

sample13.0ms (0.6%)

simplify97.0ms (4.8%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

rewrite13.0ms (0.6%)

series43.0ms (2.1%)

simplify76.0ms (3.8%)

prune44.0ms (2.2%)

localize6.0ms (0.3%)

rewrite24.0ms (1.2%)

series139.0ms (6.9%)

simplify49.0ms (2.4%)

prune51.0ms (2.5%)

localize7.0ms (0.4%)

rewrite41.0ms (2%)

series166.0ms (8.2%)

simplify55.0ms (2.7%)

prune104.0ms (5.2%)

localize7.0ms (0.3%)

rewrite23.0ms (1.2%)

series111.0ms (5.5%)

simplify64.0ms (3.2%)

prune79.0ms (3.9%)

simplify7.0ms (0.3%)

regimes33.0ms (1.7%)

bsearch0.0ms (0%)

regimes23.0ms (1.1%)

bsearch27.0ms (1.3%)

regimes10.0ms (0.5%)

bsearch0.0ms (0%)

regimes8.0ms (0.4%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample685.0ms (33.9%)

Profiling