Details

analyze1.1s (7.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample240.0ms (1.7%)

Algorithm

1×

intervals

Results

73.0ms	138×	body	1024	nan
69.0ms	129×	body	1024	valid
26.0ms	69×	body	512	valid
25.0ms	70×	body	512	nan
15.0ms	13×	body	2048	valid
7.0ms	28×	body	256	nan
7.0ms	25×	body	256	valid
3.0ms	20×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify271.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4731	55
1	4731	55

prune12.0ms (0.1%)

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

Merged error: 61.9b

Counts

2 → 1

Compiler

Compiled 133 to 102 computations (23.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(*.f64 (/.f64 PI.f64 4) f)
1.0b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
4.9b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite69.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`unpow-prod-down_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/r*_binary64` `sqr-pow_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
3×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 141

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
9.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
8.0ms	(*.f64 (/.f64 PI.f64 4) f)
8.0ms	(*.f64 (/.f64 PI.f64 4) f)

series603.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

451.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
78.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
38.0ms	(*.f64 (/.f64 PI.f64 4) f)
36.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5123	5751

prune539.0ms (3.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	3	154

Merged error: 1.4b

Counts

154 → 3

Compiler

Compiled 9109 to 6321 computations (30.6% saved)

localize85.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 PI.f64 3)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`pow-unpow_binary64` `unpow-prod-down_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
5×	`add-cbrt-cube_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
3×	`cube-prod_binary64`
1×	`rem-cube-cbrt_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 74

Calls

4 calls:

3.0ms	(pow.f64 PI.f64 4)
3.0ms	(pow.f64 PI.f64 4)
3.0ms	(pow.f64 PI.f64 3)
3.0ms	(pow.f64 PI.f64 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 3)
0.0ms	(pow.f64 PI.f64 4)

simplify43.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5373	1148

prune1.2s (8.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 1.4b

Counts

81 → 4

Compiler

Compiled 15092 to 11857 computations (21.4% saved)

localize51.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (log.f64 (+.f64 (+.f64 (+.f64 (.f64 1/512 (.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))) (+.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))) (+.f64 (.f64 1/16 (.f64 PI.f64 f)) (+.f64 (.f64 5/6 (.f64 (.f64 PI.f64 f) -1/16)) (+.f64 (.f64 1/512 (.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))) 3/4))))) (.f64 (.f64 PI.f64 1/8) (+.f64 (.f64 1/4 f) (.f64 f 1/2)))) (-.f64 -1/2 (+.f64 (.f64 PI.f64 (/.f64 (.f64 f 1/32) -1)) (+.f64 (.f64 5/96 (.f64 PI.f64 f)) (+.f64 1/4 (.f64 (.f64 (/.f64 f (*.f64 PI.f64 1/8)) (pow.f64 PI.f64 2)) 1/256))))))) (/.f64 -4 PI.f64))
0.4b	(.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))
0.4b	(.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))
0.4b	(.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))

rewrite97.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-exp-log_binary64`
47×	`add-sqr-sqrt_binary64`
38×	`prod-exp_binary64`
37×	`associate-r_binary64`
36×	`add-cbrt-cube_binary64`
25×	`associate-l_binary64`
24×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`times-frac_binary64` `div-exp_binary64`
14×	`cbrt-unprod_binary64` `unswap-sqr_binary64`
12×	`unpow-prod-down_binary64`
9×	`pow-to-exp_binary64` `pow-exp_binary64`
7×	`pow1_binary64` `cbrt-undiv_binary64`
6×	`unpow2_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `*-commutative_binary64`
3×	`associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-*r/_binary64` `log-pow_binary64`

Counts

4 → 153

Calls

4 calls:

23.0ms	(.f64 (log.f64 (+.f64 (+.f64 (+.f64 (.f64 1/512 (.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))) (+.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))) (+.f64 (.f64 1/16 (.f64 PI.f64 f)) (+.f64 (.f64 5/6 (.f64 (.f64 PI.f64 f) -1/16)) (+.f64 (.f64 1/512 (.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))) 3/4))))) (.f64 (.f64 PI.f64 1/8) (+.f64 (.f64 1/4 f) (.f64 f 1/2)))) (-.f64 -1/2 (+.f64 (.f64 PI.f64 (/.f64 (.f64 f 1/32) -1)) (+.f64 (.f64 5/96 (.f64 PI.f64 f)) (+.f64 1/4 (.f64 (.f64 (/.f64 f (*.f64 PI.f64 1/8)) (pow.f64 PI.f64 2)) 1/256))))))) (/.f64 -4 PI.f64))
11.0ms	(.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))
11.0ms	(.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))
11.0ms	(.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))

series298.0ms (2%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(.f64 (log.f64 (+.f64 (+.f64 (+.f64 (.f64 1/512 (.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))) (+.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))) (+.f64 (.f64 1/16 (.f64 PI.f64 f)) (+.f64 (.f64 5/6 (.f64 (.f64 PI.f64 f) -1/16)) (+.f64 (.f64 1/512 (.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))) 3/4))))) (.f64 (.f64 PI.f64 1/8) (+.f64 (.f64 1/4 f) (.f64 f 1/2)))) (-.f64 -1/2 (+.f64 (.f64 PI.f64 (/.f64 (.f64 f 1/32) -1)) (+.f64 (.f64 5/96 (.f64 PI.f64 f)) (+.f64 1/4 (.f64 (.f64 (/.f64 f (*.f64 PI.f64 1/8)) (pow.f64 PI.f64 2)) 1/256))))))) (/.f64 -4 PI.f64))
40.0ms	(.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))
40.0ms	(.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))
37.0ms	(.f64 (/.f64 f (.f64 PI.f64 1/8)) (pow.f64 PI.f64 2))

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5369	5438

prune1.5s (10.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	156	9	165
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	158	11	169

Merged error: 1.1b

Counts

169 → 11

Compiler

Compiled 25385 to 18681 computations (26.4% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 PI.f64 (+.f64 (.f64 -1/32 f) (*.f64 5/96 f)))
0.4b	(.f64 (.f64 PI.f64 1/8) (*.f64 f 3/4))
0.4b	(.f64 (.f64 f PI.f64) 1/96)
0.6b	(+.f64 (.f64 -1/32 f) (.f64 5/96 f))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`associate-l_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-rgt-out_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

4 calls:

8.0ms	(.f64 PI.f64 (+.f64 (.f64 -1/32 f) (*.f64 5/96 f)))
7.0ms	(.f64 (.f64 PI.f64 1/8) (*.f64 f 3/4))
6.0ms	(.f64 (.f64 f PI.f64) 1/96)
5.0ms	(+.f64 (.f64 -1/32 f) (.f64 5/96 f))

series150.0ms (1%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(.f64 (.f64 f PI.f64) 1/96)
40.0ms	(.f64 PI.f64 (+.f64 (.f64 -1/32 f) (*.f64 5/96 f)))
34.0ms	(.f64 (.f64 PI.f64 1/8) (*.f64 f 3/4))
31.0ms	(+.f64 (.f64 -1/32 f) (.f64 5/96 f))

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4885	807
1	4885	807

prune349.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	87	11	98

Merged error: 1.1b

Counts

98 → 11

Compiler

Compiled 7906 to 5753 computations (27.2% saved)

regimes98.0ms (0.7%)

Compiler: Compiled 1043 to 787 computations (24.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	52
1	48	52

end0.0ms (0%)

sample7.5s (51.7%)

Algorithm

1×

intervals

Results

2.0s	3847×	body	1024	valid
2.0s	4024×	body	1024	nan
729.0ms	1954×	body	512	valid
665.0ms	1908×	body	512	nan
571.0ms	503×	body	2048	valid
263.0ms	1009×	body	256	valid
225.0ms	956×	body	256	nan
100.0ms	687×	body	128	valid
5.0ms	6×	body	2048	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 1110 to 841 computations (24.2% saved)

Details

analyze1.1s (7.5%)

sample240.0ms (1.7%)

simplify271.0ms (1.9%)

prune12.0ms (0.1%)

localize20.0ms (0.1%)

rewrite69.0ms (0.5%)

series603.0ms (4.1%)

simplify81.0ms (0.6%)

prune539.0ms (3.7%)

localize85.0ms (0.6%)

rewrite39.0ms (0.3%)

series0.0ms (0%)

simplify43.0ms (0.3%)

prune1.2s (8.1%)

localize51.0ms (0.4%)

rewrite97.0ms (0.7%)

series298.0ms (2%)

simplify87.0ms (0.6%)

prune1.5s (10.2%)

localize37.0ms (0.3%)

rewrite39.0ms (0.3%)

series150.0ms (1%)

simplify65.0ms (0.4%)

prune349.0ms (2.4%)

regimes98.0ms (0.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.5s (51.7%)

Profiling