Details

analyze930.0ms (6.9%)

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)

sample285.0ms (2.1%)

Algorithm

1×

intervals

Results

87.0ms	124×	body	1280	valid
72.0ms	113×	body	1280	nan
40.0ms	80×	body	640	nan
31.0ms	63×	body	640	valid
17.0ms	47×	body	320	nan
12.0ms	32×	body	320	valid
7.0ms	26×	body	160	valid
2.0ms	10×	body	160	nan
1.0ms	11×	body	80	valid
0.0ms	1×	body	80	overflowed

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify253.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4749	55
1	4749	55

prune8.0ms (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: 61.2b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.8b	(/.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))))
7.5b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite237.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
61×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64` `insert-posit16`
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 → 138

Calls

4 calls:

196.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
17.0ms	(/.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))))
8.0ms	(*.f64 (/.f64 PI.f64 4) f)
8.0ms	(*.f64 (/.f64 PI.f64 4) f)

series462.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(/.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))))
135.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
43.0ms	(*.f64 (/.f64 PI.f64 4) f)
40.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify127.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4972	5403
1	4972	5403

prune388.0ms (2.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	3	151

Merged error: 1.6b

Counts

151 → 3

Compiler

Compiled 6586 to 4404 computations (33.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.4b	(.f64 (.f64 PI.f64 f) 1/12)
0.4b	(.f64 (log.f64 (-.f64 (+.f64 (.f64 (.f64 PI.f64 f) 1/12) (/.f64 4 (.f64 PI.f64 f))) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) (/.f64 -4 PI.f64))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`associate-r_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`pow1_binary64`
13×	`times-frac_binary64`
8×	`associate-l_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `div-exp_binary64` `-commutative_binary64`
2×	`div-inv_binary64`
1×	`associate-/r_binary64` `associate-r/_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 94

Calls

4 calls:

12.0ms	(.f64 (log.f64 (-.f64 (+.f64 (.f64 (.f64 PI.f64 f) 1/12) (/.f64 4 (.f64 PI.f64 f))) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) (/.f64 -4 PI.f64))
6.0ms	(.f64 (.f64 PI.f64 f) 1/12)
6.0ms	(/.f64 4 (*.f64 PI.f64 f))
5.0ms	(*.f64 PI.f64 f)

series352.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(.f64 (log.f64 (-.f64 (+.f64 (.f64 (.f64 PI.f64 f) 1/12) (/.f64 4 (.f64 PI.f64 f))) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) (/.f64 -4 PI.f64))
57.0ms	(/.f64 4 (*.f64 PI.f64 f))
50.0ms	(.f64 (.f64 PI.f64 f) 1/12)
33.0ms	(*.f64 PI.f64 f)

simplify166.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4897	2316
1	4897	2316

prune174.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	8	106
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 1.3b

Counts

109 → 10

Compiler

Compiled 3539 to 2203 computations (37.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.3b	(/.f64 (.f64 (log.f64 (-.f64 (+.f64 (.f64 (.f64 PI.f64 f) 1/12) (/.f64 4 (.f64 PI.f64 f))) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) -4) PI.f64)
0.4b	(.f64 (.f64 PI.f64 f) 1/12)

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `times-frac_binary64`
4×	`pow-prod-down_binary64` `associate-/r_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `associate-/l_binary64` `div-exp_binary64` `insert-posit16`
2×	`clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`unswap-sqr_binary64`

Counts

4 → 82

Calls

4 calls:

9.0ms	(/.f64 (.f64 (log.f64 (-.f64 (+.f64 (.f64 (.f64 PI.f64 f) 1/12) (/.f64 4 (.f64 PI.f64 f))) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) -4) PI.f64)
7.0ms	(.f64 (.f64 PI.f64 f) 1/12)
6.0ms	(/.f64 4 (*.f64 PI.f64 f))
5.0ms	(*.f64 PI.f64 f)

series318.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(/.f64 (.f64 (log.f64 (-.f64 (+.f64 (.f64 (.f64 PI.f64 f) 1/12) (/.f64 4 (.f64 PI.f64 f))) (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/2880))) -4) PI.f64)
46.0ms	(/.f64 4 (*.f64 PI.f64 f))
44.0ms	(.f64 (.f64 PI.f64 f) 1/12)
28.0ms	(*.f64 PI.f64 f)

simplify127.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4910	1690
1	4910	1690

prune145.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 1.2b

Counts

104 → 10

Compiler

Compiled 3037 to 1889 computations (37.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64)))
0.4b	(*.f64 (/.f64 4 PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64))))
1.0b	(pow.f64 PI.f64 3)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
35×	`log-prod_binary64`
32×	`add-cube-cbrt_binary64`
28×	`times-frac_binary64`
16×	`pow1_binary64`
13×	`associate--r+_binary64` `add-exp-log_binary64` `associate-l_binary64`
10×	`add-cbrt-cube_binary64`
9×	`log-pow_binary64` `associate--l+_binary64`
8×	`associate-r_binary64` `distribute-lft-out--_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `log-div_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `sub-neg_binary64` `flip3--_binary64` `associate--r-_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `div-inv_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `rem-log-exp_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `frac-times_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64` `unpow3_binary64` `associate-l/_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 135

Calls

4 calls:

15.0ms	(*.f64 (/.f64 4 PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64))))
8.0ms	(-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64)))
3.0ms	(log.f64 (/.f64 4 PI.f64))
3.0ms	(pow.f64 PI.f64 3)

series428.0ms (3.2%)

Counts

4 → 8

Calls

4 calls:

251.0ms	(*.f64 (/.f64 4 PI.f64) (-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64))))
177.0ms	(-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64)))
0.0ms	(log.f64 (/.f64 4 PI.f64))
0.0ms	(pow.f64 PI.f64 3)

simplify119.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5019	2432

prune269.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	2	6	8
Picked	1	0	1
Done	1	0	1
Total	142	11	153

Merged error: 1.2b

Counts

153 → 11

Compiler

Compiled 4928 to 3126 computations (36.6% saved)

regimes45.0ms (0.3%)

Compiler: Compiled 473 to 339 computations (28.3% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	52
1	41	52

end0.0ms (0%)

sample8.5s (62.9%)

Algorithm

1×

intervals

Results

2.4s	3524×	body	1280	valid
1.9s	2993×	body	1280	nan
1.2s	2422×	body	640	valid
1.1s	2447×	body	640	nan
441.0ms	1270×	body	320	nan
439.0ms	1199×	body	320	valid
161.0ms	633×	body	160	valid
54.0ms	235×	body	160	nan
31.0ms	222×	body	80	valid
1.0ms	7×	body	80	overflowed

Compiler

Compiled 540 to 394 computations (27% saved)

Details

analyze930.0ms (6.9%)

sample285.0ms (2.1%)

simplify253.0ms (1.9%)

prune8.0ms (0.1%)

localize20.0ms (0.1%)

rewrite237.0ms (1.8%)

series462.0ms (3.4%)

simplify127.0ms (0.9%)

prune388.0ms (2.9%)

localize14.0ms (0.1%)

rewrite32.0ms (0.2%)

series352.0ms (2.6%)

simplify166.0ms (1.2%)

prune174.0ms (1.3%)

localize14.0ms (0.1%)

rewrite29.0ms (0.2%)

series318.0ms (2.4%)

simplify127.0ms (0.9%)

prune145.0ms (1.1%)

localize20.0ms (0.1%)

rewrite35.0ms (0.3%)

series428.0ms (3.2%)

simplify119.0ms (0.9%)

prune269.0ms (2%)

regimes45.0ms (0.3%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample8.5s (62.9%)

Profiling