Details

analyze1.2s (17%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
13.1%	74.3%	12.7%	12
16.1%	70.5%	13.5%	13
18.6%	68%	13.5%	14

sample88.0ms (1.3%)

Algorithm

1×

intervals

Results

25.0ms	41×	body	1280	valid
18.0ms	52×	body	640	valid
8.0ms	112×	body	80	valid
8.0ms	33×	body	320	valid
4.0ms	3×	body	2560	valid
2.0ms	15×	body	160	valid
2.0ms	45×	body	80	nan
2.0ms	10×	body	320	nan
2.0ms	30×	body	80	overflowed
1.0ms	4×	body	640	nan
1.0ms	2×	body	1280	nan
0.0ms	4×	body	160	nan

simplify276.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (273.0ms)

Iter	Nodes	Cost
0	3730	13
1	3730	13

prune8.0ms (0.1%)

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

Merged error: 24.3b

Counts

2 → 1

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (exp.f64 z))
0.0b	(/.f64 (log.f64 (+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z)))) t)
1.3b	(+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z)))
2.3b	(log.f64 (+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
9×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`associate-/l*_binary64` `log-div_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-r_binary64` `log-prod_binary64` `associate-l*_binary64` `flip-+_binary64`
2×	`div-sub_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

9.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z)))) t)
8.0ms	(+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z)))
7.0ms	(log.f64 (+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z))))
6.0ms	(*.f64 y (exp.f64 z))

series85.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z)))) t)
17.0ms	(log.f64 (+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z))))
8.0ms	(+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z)))
6.0ms	(*.f64 y (exp.f64 z))

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5127	1261

prune160.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	85	6	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 6.1b

Counts

92 → 6

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 z (+.f64 (.f64 0.5 z) 1.0))
3.5b	(.f64 y (.f64 z (+.f64 (*.f64 0.5 z) 1.0)))
7.1b	(/.f64 (+.f64 (log.f64 1.0) (.f64 y (.f64 z (+.f64 (*.f64 0.5 z) 1.0)))) t)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`times-frac_binary64`
6×	`associate-r/_binary64` `associate-l*_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 75

Calls

3 calls:

9.0ms	(.f64 y (.f64 z (+.f64 (*.f64 0.5 z) 1.0)))
7.0ms	(.f64 z (+.f64 (.f64 0.5 z) 1.0))
7.0ms	(/.f64 (+.f64 (log.f64 1.0) (.f64 y (.f64 z (+.f64 (*.f64 0.5 z) 1.0)))) t)

series51.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(/.f64 (+.f64 (log.f64 1.0) (.f64 y (.f64 z (+.f64 (*.f64 0.5 z) 1.0)))) t)
11.0ms	(.f64 y (.f64 z (+.f64 (*.f64 0.5 z) 1.0)))
9.0ms	(.f64 z (+.f64 (.f64 0.5 z) 1.0))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4946	1137
1	4946	1137

prune169.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	79	11	90

Merged error: 6.1b

Counts

90 → 11

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
1.1b	(.f64 (.f64 z (+.f64 1.0 (*.f64 z 0.5))) (cbrt.f64 y))
2.8b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 z (+.f64 1.0 (*.f64 z 0.5))) (cbrt.f64 y)))
7.1b	(/.f64 (+.f64 (log.f64 1.0) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 z (+.f64 1.0 (*.f64 z 0.5))) (cbrt.f64 y)))) t)

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
30×	`pow1_binary64`
20×	`add-cbrt-cube_binary64`
18×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`associate-r_binary64`
6×	`associate-*r/_binary64` `cbrt-prod_binary64`
4×	`add-log-exp_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `associate-l_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `pow1/3_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 93

Calls

4 calls:

17.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 z (+.f64 1.0 (*.f64 z 0.5))) (cbrt.f64 y)))
8.0ms	(.f64 (.f64 z (+.f64 1.0 (*.f64 z 0.5))) (cbrt.f64 y))
7.0ms	(/.f64 (+.f64 (log.f64 1.0) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 z (+.f64 1.0 (*.f64 z 0.5))) (cbrt.f64 y)))) t)
1.0ms	(cbrt.f64 y)

series103.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(/.f64 (+.f64 (log.f64 1.0) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 z (+.f64 1.0 (*.f64 z 0.5))) (cbrt.f64 y)))) t)
30.0ms	(.f64 (.f64 z (+.f64 1.0 (*.f64 z 0.5))) (cbrt.f64 y))
20.0ms	(cbrt.f64 y)
17.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (.f64 z (+.f64 1.0 (*.f64 z 0.5))) (cbrt.f64 y)))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4935	1345
1	4935	1345

prune181.0ms (2.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	104	12	116

Merged error: 6.1b

Counts

116 → 12

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (exp.f64 z))
0.1b	(.f64 (log.f64 (+.f64 (-.f64 1.0 y) (.f64 y (exp.f64 z)))) (/.f64 1 t))
1.3b	(+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z)))
2.3b	(log.f64 (+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
16×	`-un-lft-identity_binary64` `associate-r*_binary64`
15×	`add-cube-cbrt_binary64` `add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `times-frac_binary64`
10×	`pow1_binary64`
9×	`add-log-exp_binary64`
7×	`associate-l_binary64`
5×	`prod-exp_binary64`
4×	`unswap-sqr_binary64`
3×	`cbrt-unprod_binary64` `log-prod_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `log-pow_binary64` `div-exp_binary64` `log-div_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `associate-*r/_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

9.0ms	(.f64 (log.f64 (+.f64 (-.f64 1.0 y) (.f64 y (exp.f64 z)))) (/.f64 1 t))
7.0ms	(+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z)))
7.0ms	(log.f64 (+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z))))
5.0ms	(*.f64 y (exp.f64 z))

series85.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(.f64 (log.f64 (+.f64 (-.f64 1.0 y) (.f64 y (exp.f64 z)))) (/.f64 1 t))
17.0ms	(log.f64 (+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z))))
8.0ms	(+.f64 (-.f64 1.0 y) (*.f64 y (exp.f64 z)))
6.0ms	(*.f64 y (exp.f64 z))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4961	1177
1	4961	1177

prune117.0ms (1.7%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	93	14	107

Merged error: 6.1b

Counts

107 → 14

regimes1.2s (17.7%)

Accuracy

Total 4.3b remaining (48.8%)

Threshold costs 0b (0%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	214	36
1	214	36

end0.0ms (0%)

sample2.7s (39.4%)

Algorithm

1×

intervals

Results

866.0ms	1428×	body	1280	valid
556.0ms	1600×	body	640	valid
261.0ms	3489×	body	80	valid
209.0ms	939×	body	320	valid
94.0ms	68×	body	2560	valid
79.0ms	1542×	body	80	nan
66.0ms	476×	body	160	valid
65.0ms	261×	body	640	nan
48.0ms	840×	body	80	overflowed
39.0ms	105×	body	1280	nan
35.0ms	199×	body	320	nan
11.0ms	102×	body	160	nan
1.0ms	18×	body	80	invalid
0.0ms	1×	body	640	invalid
0.0ms	1×	body	320	invalid

Details

analyze1.2s (17%)

sample88.0ms (1.3%)

simplify276.0ms (4.1%)

prune8.0ms (0.1%)

localize14.0ms (0.2%)

rewrite31.0ms (0.5%)

series85.0ms (1.3%)

simplify61.0ms (0.9%)

prune160.0ms (2.4%)

localize11.0ms (0.2%)

rewrite26.0ms (0.4%)

series51.0ms (0.7%)

simplify52.0ms (0.8%)

prune169.0ms (2.5%)

localize15.0ms (0.2%)

rewrite38.0ms (0.6%)

series103.0ms (1.5%)

simplify69.0ms (1%)

prune181.0ms (2.7%)

localize14.0ms (0.2%)

rewrite31.0ms (0.5%)

series85.0ms (1.2%)

simplify72.0ms (1.1%)

prune117.0ms (1.7%)

regimes1.2s (17.7%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.7s (39.4%)

Profiling