Details

analyze2.3s (3.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample94.0ms (0.1%)

Algorithm

1×

intervals

Results

46.0ms	84×	body	1024	valid
15.0ms	41×	body	512	valid
9.0ms	107×	body	128	valid
5.0ms	7×	body	2048	valid
3.0ms	17×	body	256	valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify810.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (455.0ms)

Iter	Nodes	Cost
0	4840	8
1	4840	8

prune84.0ms (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: 0.0b

Counts

2 → 2

Compiler

Compiled 22 to 21 computations (4.5% saved)

localize68.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0b	(+.f64 1 (exp.f64 x))

rewrite190.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 28

Calls

2 calls:

80.0ms	(+.f64 1 (exp.f64 x))
15.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series218.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

115.0ms	(+.f64 1 (exp.f64 x))
102.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

simplify419.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (380.0ms)

Iter	Nodes	Cost
0	5088	368

prune496.0ms (0.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	21	13	34
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	22	14	36

Merged error: 0b

Counts

36 → 14

Compiler

Compiled 478 to 358 computations (25.1% saved)

localize43.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
0.0b	(pow.f64 (exp.f64 x) 2)
0.1b	(pow.f64 (exp.f64 x) 3)
3.7b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

rewrite171.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`sqrt-prod_binary64`
22×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
13×	`distribute-lft-out_binary64`
8×	`pow-pow_binary64`
7×	`pow1_binary64` `unpow-prod-down_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `exp-prod_binary64`
5×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
4×	`add-exp-log_binary64` `difference-of-squares_binary64`
3×	`unpow2_binary64` `sqr-pow_binary64` `cancel-sign-sub-inv_binary64` `cube-prod_binary64`
2×	`pow-to-exp_binary64` `associate-/r/_binary64` `rem-sqrt-square_binary64` `pow-exp_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `sqrt-pow1_binary64` `rem-cube-cbrt_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `unpow3_binary64` `sqrt-div_binary64` `cube-mult_binary64`

Counts

4 → 105

Calls

4 calls:

64.0ms	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
33.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
20.0ms	(pow.f64 (exp.f64 x) 3)
6.0ms	(pow.f64 (exp.f64 x) 2)

series710.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

472.0ms	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
102.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
84.0ms	(pow.f64 (exp.f64 x) 3)
48.0ms	(pow.f64 (exp.f64 x) 2)

simplify171.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	5231	2261

prune2.8s (4.5%)

Pruning

46 alts after pruning (45 fresh and 1 done)

	Pruned	Kept	Total
New	81	36	117
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	85	46	131

Merged error: 0b

Counts

131 → 46

Compiler

Compiled 3764 to 2559 computations (32% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
0.0b	(exp.f64 (*.f64 x 3))
0.0b	(pow.f64 (exp.f64 x) 2)
3.7b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

rewrite162.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`sqrt-prod_binary64`
21×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
13×	`distribute-lft-out_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64`
5×	`distribute-lft-out--_binary64`
4×	`pow-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64` `difference-of-squares_binary64` `exp-prod_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `cancel-sign-sub-inv_binary64`
2×	`sqr-pow_binary64` `associate-/r/_binary64` `rem-sqrt-square_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `div-inv_binary64` `exp-lft-cube_binary64` `flip--_binary64` `exp-to-pow_binary64` `flip-+_binary64` `pow-exp_binary64` `sqrt-div_binary64`

Counts

4 → 90

Calls

4 calls:

76.0ms	(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
31.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
13.0ms	(pow.f64 (exp.f64 x) 2)
4.0ms	(exp.f64 (*.f64 x 3))

series529.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

358.0ms	(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
87.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
56.0ms	(pow.f64 (exp.f64 x) 2)
26.0ms	(exp.f64 (*.f64 x 3))

simplify167.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	5018	2145

prune3.3s (5.1%)

Pruning

45 alts after pruning (43 fresh and 2 done)

	Pruned	Kept	Total
New	89	13	102
Fresh	14	30	44
Picked	0	1	1
Done	0	1	1
Total	103	45	148

Merged error: 0b

Counts

148 → 45

Compiler

Compiled 3435 to 2409 computations (29.9% saved)

localize53.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(*.f64 (exp.f64 x) (pow.f64 (exp.f64 x) 2))
3.7b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

rewrite124.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
11×	`unpow-prod-down_binary64`
8×	`associate-r_binary64` `pow-pow_binary64`
7×	`pow1_binary64` `unpow2_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
5×	`sqr-pow_binary64` `add-exp-log_binary64`
4×	`unswap-sqr_binary64` `difference-of-squares_binary64`
3×	`pow-to-exp_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `distribute-rgt-out--_binary64` `cube-unmult_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

46.0ms	(*.f64 (exp.f64 x) (pow.f64 (exp.f64 x) 2))
19.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
17.0ms	(pow.f64 (exp.f64 x) 2)
11.0ms	(pow.f64 (exp.f64 x) 2)

series279.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(*.f64 (exp.f64 x) (pow.f64 (exp.f64 x) 2))
82.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
50.0ms	(pow.f64 (exp.f64 x) 2)
45.0ms	(pow.f64 (exp.f64 x) 2)

simplify288.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (244.0ms)

Iter	Nodes	Cost
0	4940	902
1	4940	902

prune3.7s (5.8%)

Pruning

55 alts after pruning (52 fresh and 3 done)

	Pruned	Kept	Total
New	84	19	103
Fresh	9	33	42
Picked	0	1	1
Done	0	2	2
Total	93	55	148

Merged error: 0b

Counts

148 → 55

Compiler

Compiled 2326 to 1376 computations (40.8% saved)

regimes4.5s (7.1%)

Compiler: Compiled 12399 to 9296 computations (25% saved)

bsearch17.8s (28%)

simplify24.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	37
1	27	37

end0.0ms (0%)

sample24.0s (37.7%)

Algorithm

1×

intervals

Results

2.9s	2638×	body	1024	valid
863.0ms	1347×	body	512	valid
513.0ms	3088×	body	128	valid
339.0ms	286×	body	2048	valid
233.0ms	641×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 4250 to 3185 computations (25.1% saved)

Pareto

0.0

Details

analyze2.3s (3.6%)

sample94.0ms (0.1%)

simplify810.0ms (1.3%)

prune84.0ms (0.1%)

localize68.0ms (0.1%)

rewrite190.0ms (0.3%)

series218.0ms (0.3%)

simplify419.0ms (0.7%)

prune496.0ms (0.8%)

localize43.0ms (0.1%)

rewrite171.0ms (0.3%)

series710.0ms (1.1%)

simplify171.0ms (0.3%)

prune2.8s (4.5%)

localize59.0ms (0.1%)

rewrite162.0ms (0.3%)

series529.0ms (0.8%)

simplify167.0ms (0.3%)

prune3.3s (5.1%)

localize53.0ms (0.1%)

rewrite124.0ms (0.2%)

series279.0ms (0.4%)

simplify288.0ms (0.5%)

prune3.7s (5.8%)

regimes4.5s (7.1%)

bsearch17.8s (28%)

simplify24.0ms (0%)

end0.0ms (0%)

sample24.0s (37.7%)

Profiling