Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample69.0ms (0.5%)

Algorithm

1×

intervals

Results

52.0ms	256×	body	128	valid
3.0ms	266×	pre	128	true
2.0ms	10×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify242.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5512	47

prune14.0ms (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: 3.0b

Counts

2 → 2

Compiler

Compiled 296 to 201 computations (32.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
0.5b	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
2.7b	(exp.f64 (*.f64 x x))

rewrite106.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

263×	`times-frac_binary64_2149`
157×	`add-sqr-sqrt_binary64_2165`
148×	`*-un-lft-identity_binary64_2143`
143×	`add-cube-cbrt_binary64_2178`
70×	`associate-l_binary64_2084`
67×	`sqrt-prod_binary64_2159`
22×	`associate-/l*_binary64_2088`
18×	`add-cbrt-cube_binary64_2179`
16×	`add-exp-log_binary64_2181`
9×	`div-inv_binary64_2140`
7×	`pow1_binary64_2204`
6×	`cbrt-undiv_binary64_2177` `add-log-exp_binary64_2182` `div-exp_binary64_2194`
5×	`associate-r_binary64_2083`
4×	`unswap-sqr_binary64_2111`
3×	`associate-/r*_binary64_2087` `cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `distribute-lft-out_binary64_2094`
2×	`frac-times_binary64_2153` `associate-*r/_binary64_2085` `flip3-+_binary64_2146` `flip-+_binary64_2117`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `clear-num_binary64_2142` `distribute-rgt-in_binary64_2093` `exp-prod_binary64_2195` `pow-prod-down_binary64_2214` `associate-l/_binary64_2086` `rem-exp-log_binary64_2183` `sqrt-pow1_binary64_2161` `exp-to-pow_binary64_2205` `-commutative_binary64_2074` `distribute-lft-in_binary64_2092` `frac-2neg_binary64_2154` `associate-/l/_binary64_2090`

Counts

4 → 230

Calls

4 calls:

47.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
11.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

series333.0ms (2.4%)

Counts

4 → 10

Calls

4 calls:

185.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
135.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
13.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify112.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5016	9372

prune6.0s (43.6%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	210	30	240
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	212	30	242

Merged error: 0.2b

Counts

242 → 30

Compiler

Compiled 137303 to 79568 computations (42% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2165`
12×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
8×	`pow1_binary64_2204` `pow-pow_binary64_2215`
6×	`pow-unpow_binary64_2220` `unpow-prod-down_binary64_2222` `exp-prod_binary64_2195` `sqrt-prod_binary64_2159`
4×	`add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `pow-to-exp_binary64_2212` `sqr-pow_binary64_2115` `sqrt-pow1_binary64_2161` `pow-exp_binary64_2211`

Counts

4 → 66

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 x) x)
4.0ms	(pow.f64 (exp.f64 x) x)
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series66.0ms (0.5%)

Counts

4 → 8

Calls

4 calls:

35.0ms	(pow.f64 (exp.f64 x) x)
31.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5285	660

prune565.0ms (4.1%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	4	25	29
Picked	1	0	1
Done	0	0	0
Total	75	29	104

Merged error: 0.2b

Counts

104 → 29

Compiler

Compiled 13665 to 7417 computations (45.7% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)
3.1b	(pow.f64 (exp.f64 1) (*.f64 x x))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_2165`
11×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
8×	`pow1_binary64_2204` `pow-pow_binary64_2215`
6×	`unpow-prod-down_binary64_2222` `exp-prod_binary64_2195` `sqrt-prod_binary64_2159`
4×	`add-log-exp_binary64_2182` `pow-unpow_binary64_2220` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `pow-to-exp_binary64_2212` `sqr-pow_binary64_2115` `sqrt-pow1_binary64_2161` `pow-exp_binary64_2211`

Counts

4 → 64

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 1) (*.f64 x x))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series48.0ms (0.3%)

Counts

4 → 8

Calls

4 calls:

31.0ms	(pow.f64 (exp.f64 x) x)
16.0ms	(pow.f64 (exp.f64 1) (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5026	562

prune183.0ms (1.3%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	28	28
Picked	0	1	1
Done	0	0	0
Total	72	29	101

Merged error: 0.2b

Counts

101 → 29

Compiler

Compiled 4568 to 2183 computations (52.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
0.5b	(/.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite108.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64_2165`
51×	`times-frac_binary64_2149`
46×	`associate-l_binary64_2084`
43×	`*-un-lft-identity_binary64_2143`
38×	`add-cube-cbrt_binary64_2178`
28×	`add-exp-log_binary64_2181`
27×	`sqrt-prod_binary64_2159`
23×	`unpow-prod-down_binary64_2222`
18×	`add-cbrt-cube_binary64_2179`
11×	`div-exp_binary64_2194`
9×	`sqr-pow_binary64_2115`
8×	`pow1_binary64_2204` `prod-exp_binary64_2192`
7×	`unswap-sqr_binary64_2111`
5×	`cbrt-undiv_binary64_2177` `associate-r_binary64_2083` `associate-/l/_binary64_2090`
4×	`add-log-exp_binary64_2182` `frac-times_binary64_2153` `cbrt-unprod_binary64_2176` `pow-pow_binary64_2215` `associate-*r/_binary64_2085` `flip3-+_binary64_2146` `flip-+_binary64_2117`
3×	`associate-/r*_binary64_2087` `pow-unpow_binary64_2220` `exp-prod_binary64_2195` `pow-to-exp_binary64_2212` `distribute-lft-out_binary64_2094` `pow-exp_binary64_2211`
2×	`div-inv_binary64_2140` `associate-*l/_binary64_2086`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `clear-num_binary64_2142` `distribute-rgt-in_binary64_2093` `associate-/l_binary64_2088` `pow-prod-down_binary64_2214` `sqrt-pow1_binary64_2161` `-commutative_binary64_2074` `distribute-lft-in_binary64_2092` `frac-2neg_binary64_2154`

Counts

4 → 143

Calls

4 calls:

45.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
36.0ms	(/.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))) (fabs.f64 x))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)

series405.0ms (3%)

Counts

4 → 10

Calls

4 calls:

219.0ms	(/.f64 (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))) (fabs.f64 x))
153.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
33.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

simplify109.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4978	6035
1	4978	6035

prune2.1s (15.1%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	147	6	153
Fresh	6	21	27
Picked	1	0	1
Done	0	1	1
Total	154	28	182

Merged error: 0.2b

Counts

182 → 28

Compiler

Compiled 47466 to 27951 computations (41.1% saved)

regimes122.0ms (0.9%)

Compiler: Compiled 1395 to 843 computations (39.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	65
1	33	65

end0.0ms (0%)

sample2.9s (21.1%)

Algorithm

1×

intervals

Results

1.7s	8000×	body	128	valid
99.0ms	8127×	pre	128	true
26.0ms	127×	body	128	invalid

Compiler

Compiled 1539 to 938 computations (39.1% saved)

Details

analyze9.0ms (0.1%)

sample69.0ms (0.5%)

simplify242.0ms (1.8%)

prune14.0ms (0.1%)

localize23.0ms (0.2%)

rewrite106.0ms (0.8%)

series333.0ms (2.4%)

simplify112.0ms (0.8%)

prune6.0s (43.6%)

localize26.0ms (0.2%)

rewrite19.0ms (0.1%)

series66.0ms (0.5%)

simplify55.0ms (0.4%)

prune565.0ms (4.1%)

localize37.0ms (0.3%)

rewrite19.0ms (0.1%)

series48.0ms (0.3%)

simplify72.0ms (0.5%)

prune183.0ms (1.3%)

localize25.0ms (0.2%)

rewrite108.0ms (0.8%)

series405.0ms (3%)

simplify109.0ms (0.8%)

prune2.1s (15.1%)

regimes122.0ms (0.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (21.1%)

Profiling