Details

analyze921.0ms (6.3%)

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)

sample258.0ms (1.8%)

Algorithm

1×

intervals

Results

76.0ms	110×	body	1280	valid
52.0ms	84×	body	1280	nan
43.0ms	88×	body	640	valid
40.0ms	82×	body	640	nan
13.0ms	35×	body	320	nan
9.0ms	25×	body	320	valid
7.0ms	26×	body	160	valid
2.0ms	7×	body	160	nan
1.0ms	7×	body	80	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify232.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4783	55
1	4783	55

prune14.0ms (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: 61.4b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(log.f64 (/.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)))))
1.2b	(/.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))))
6.0b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite246.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
37×	`add-cube-cbrt_binary64`
34×	`log-prod_binary64`
30×	`difference-of-squares_binary64`
15×	`distribute-lft-out_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`
11×	`add-cbrt-cube_binary64`
10×	`sqr-pow_binary64` `unpow-prod-down_binary64` `distribute-lft-out--_binary64`
7×	`associate-/r*_binary64` `pow1_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`flip3--_binary64` `associate-r_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 151

Calls

4 calls:

195.0ms	(-.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))))
16.0ms	(log.f64 (/.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)

series870.0ms (6%)

Counts

4 → 12

Calls

4 calls:

463.0ms	(log.f64 (/.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)))))
253.0ms	(/.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))))
112.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
41.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify156.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5100	8590

prune455.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	5	164

Merged error: 1.8b

Counts

164 → 5

Compiler

Compiled 7734 to 5227 computations (32.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 f f) (pow.f64 PI.f64 2))
0.4b	(.f64 (-.f64 (+.f64 (.f64 1/48 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (log.f64 (/.f64 4 PI.f64))) (+.f64 (log.f64 f) (.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 PI.f64 4))))) (/.f64 -4 PI.f64))
1.6b	(pow.f64 PI.f64 4)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
26×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
19×	`times-frac_binary64`
14×	`add-cbrt-cube_binary64`
13×	`log-prod_binary64`
11×	`prod-exp_binary64`
8×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64` `frac-sub_binary64`
7×	`unpow-prod-down_binary64`
6×	`associate-l_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-*l/_binary64`
5×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `unpow2_binary64` `rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `associate-*r/_binary64` `pow-pow_binary64` `log-pow_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `pow2_binary64`

Counts

4 → 121

Calls

4 calls:

29.0ms	(.f64 (-.f64 (+.f64 (.f64 1/48 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (log.f64 (/.f64 4 PI.f64))) (+.f64 (log.f64 f) (.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 PI.f64 4))))) (/.f64 -4 PI.f64))
9.0ms	(.f64 (.f64 f f) (pow.f64 PI.f64 2))
3.0ms	(log.f64 (/.f64 4 PI.f64))
3.0ms	(pow.f64 PI.f64 4)

series226.0ms (1.6%)

Counts

4 → 8

Calls

4 calls:

163.0ms	(.f64 (-.f64 (+.f64 (.f64 1/48 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (log.f64 (/.f64 4 PI.f64))) (+.f64 (log.f64 f) (.f64 7/23040 (.f64 (pow.f64 f 4) (pow.f64 PI.f64 4))))) (/.f64 -4 PI.f64))
63.0ms	(.f64 (.f64 f f) (pow.f64 PI.f64 2))
0.0ms	(log.f64 (/.f64 4 PI.f64))
0.0ms	(pow.f64 PI.f64 4)

simplify148.0ms (1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5000	4880

prune406.0ms (2.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	119	10	129
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	120	14	134

Merged error: 1.5b

Counts

134 → 14

Compiler

Compiled 6846 to 4770 computations (30.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (.f64 4 (/.f64 (log.f64 f) PI.f64)) (+.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64)) (.f64 (.f64 PI.f64 (*.f64 f f)) 1/12)))
0.3b	(/.f64 (log.f64 f) PI.f64)
1.0b	(pow.f64 PI.f64 3)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
13×	`log-prod_binary64`
10×	`pow1_binary64` `add-exp-log_binary64`
9×	`add-log-exp_binary64`
7×	`add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`associate-/l*_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
2×	`diff-log_binary64` `rem-log-exp_binary64` `associate-*r/_binary64` `div-inv_binary64` `div-exp_binary64` `frac-sub_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `log-div_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 97

Calls

4 calls:

17.0ms	(-.f64 (.f64 4 (/.f64 (log.f64 f) PI.f64)) (+.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64)) (.f64 (.f64 PI.f64 (*.f64 f f)) 1/12)))
5.0ms	(/.f64 (log.f64 f) PI.f64)
4.0ms	(log.f64 (/.f64 4 PI.f64))
3.0ms	(pow.f64 PI.f64 3)

series541.0ms (3.7%)

Counts

4 → 8

Calls

4 calls:

431.0ms	(-.f64 (.f64 4 (/.f64 (log.f64 f) PI.f64)) (+.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64)) (.f64 (.f64 PI.f64 (*.f64 f f)) 1/12)))
110.0ms	(/.f64 (log.f64 f) PI.f64)
0.0ms	(log.f64 (/.f64 4 PI.f64))
0.0ms	(pow.f64 PI.f64 3)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4936	2172
1	4936	2172

prune243.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	106	13	119

Merged error: 1.5b

Counts

119 → 13

Compiler

Compiled 5123 to 3263 computations (36.3% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(log.f64 (/.f64 4 PI.f64))
2.0b	(log.f64 (/.f64 4 PI.f64))
2.0b	(log.f64 (/.f64 4 PI.f64))
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`log-prod_binary64`
36×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
8×	`pow1_binary64` `rem-log-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64` `insert-posit16`

Counts

4 → 100

Calls

4 calls:

3.0ms	(log.f64 (/.f64 4 PI.f64))
3.0ms	(log.f64 (/.f64 4 PI.f64))
3.0ms	(log.f64 (/.f64 4 PI.f64))
3.0ms	(log.f64 (/.f64 4 PI.f64))

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(log.f64 (/.f64 4 PI.f64))
0.0ms	(log.f64 (/.f64 4 PI.f64))
0.0ms	(log.f64 (/.f64 4 PI.f64))
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5951	1948

prune775.0ms (5.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	104	13	117

Merged error: 1.5b

Counts

117 → 13

Compiler

Compiled 11504 to 7963 computations (30.8% saved)

regimes94.0ms (0.6%)

Compiler: Compiled 1032 to 767 computations (25.7% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	121	55
1	121	55

end0.0ms (0%)

sample8.6s (58.9%)

Algorithm

1×

intervals

Results

2.3s	3444×	body	1280	valid
1.7s	2833×	body	1280	nan
1.2s	2422×	body	640	valid
1.1s	2397×	body	640	nan
436.0ms	1203×	body	320	valid
421.0ms	1239×	body	320	nan
173.0ms	679×	body	160	valid
54.0ms	229×	body	160	nan
34.0ms	252×	body	80	valid
0.0ms	1×	body	80	overflowed

Compiler

Compiled 1101 to 823 computations (25.2% saved)

Details

analyze921.0ms (6.3%)

sample258.0ms (1.8%)

simplify232.0ms (1.6%)

prune14.0ms (0.1%)

localize20.0ms (0.1%)

rewrite246.0ms (1.7%)

series870.0ms (6%)

simplify156.0ms (1.1%)

prune455.0ms (3.1%)

localize23.0ms (0.2%)

rewrite50.0ms (0.3%)

series226.0ms (1.6%)

simplify148.0ms (1%)

prune406.0ms (2.8%)

localize22.0ms (0.2%)

rewrite31.0ms (0.2%)

series541.0ms (3.7%)

simplify76.0ms (0.5%)

prune243.0ms (1.7%)

localize39.0ms (0.3%)

rewrite17.0ms (0.1%)

series0.0ms (0%)

simplify119.0ms (0.8%)

prune775.0ms (5.3%)

regimes94.0ms (0.6%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample8.6s (58.9%)

Profiling