Details

analyze1.3s (7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55
0	1	1
1	1	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)

sample223.0ms (1.2%)

Algorithm

1×

intervals

Results

61.0ms	121×	body	1024	valid
61.0ms	132×	body	1024	nan
25.0ms	61×	body	512	valid
19.0ms	58×	body	512	nan
13.0ms	12×	body	2048	valid
10.0ms	43×	body	256	valid
8.0ms	35×	body	256	nan
2.0ms	19×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune10.0ms (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

Error

61.9b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize19.0ms (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))))
7.0b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite622.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

61.9b

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×	`sqr-pow_binary64` `cancel-sign-sub-inv_binary64` `associate-/r*_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `associate-r_binary64`
4×	`associate-/l*_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
3×	`div-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
2×	`flip3--_binary64` `flip--_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `frac-2neg_binary64` `clear-num_binary64` `flip3-+_binary64` `flip-+_binary64`

Counts

4 → 141

Calls

4 calls:

13.0ms	(/.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 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 5775 to 3852 computations (33.3% saved)

series407.0ms (2.2%)

Error

1.3b

Counts

4 → 12

Calls

4 calls:

217.0ms	(/.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))))
76.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
49.0ms	(*.f64 (/.f64 PI.f64 4) f)
44.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1112 to 841 computations (24.4% saved)

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5172	5387

prune363.0ms (1.9%)

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

Error

1.2b

Counts

154 → 3

Compiler

Compiled 5282 to 3538 computations (33% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
0.3b	(.f64 f (.f64 PI.f64 1/2))
0.3b	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
0.4b	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))

rewrite195.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

33×	`add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
22×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
16×	`times-frac_binary64`
14×	`associate-r_binary64`
13×	`pow1_binary64`
11×	`prod-exp_binary64`
8×	`cbrt-unprod_binary64`
7×	`div-exp_binary64` `associate-l_binary64` `log-prod_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64`
3×	`div-inv_binary64` `associate-/l*_binary64`
2×	`unswap-sqr_binary64` `log-pow_binary64` `*-commutative_binary64`
1×	`associate-r/_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/r_binary64` `log-div_binary64`

Counts

4 → 94

Calls

4 calls:

10.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
6.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
5.0ms	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
5.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 1666 to 1268 computations (23.9% saved)

series392.0ms (2.1%)

Error

1.0b

Counts

4 → 12

Calls

4 calls:

173.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
119.0ms	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
47.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
40.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 376 to 328 computations (12.8% saved)

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5045	1497

prune155.0ms (0.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	93	13	106
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	94	15	109

Error

0.9b

Counts

109 → 15

Compiler

Compiled 1557 to 1127 computations (27.6% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
0.3b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.3b	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)

rewrite162.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

21×	`add-sqr-sqrt_binary64`
19×	`add-exp-log_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
18×	`times-frac_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`
7×	`associate-/l*_binary64` `log-prod_binary64`
5×	`div-exp_binary64` `log-pow_binary64`
4×	`add-log-exp_binary64` `associate-/r*_binary64`
3×	`cbrt-undiv_binary64` `div-inv_binary64` `prod-exp_binary64` `associate-l_binary64` `associate-r_binary64` `rem-log-exp_binary64`
2×	`frac-2neg_binary64` `log-div_binary64` `clear-num_binary64` `cbrt-unprod_binary64`
1×	`div-sub_binary64` `pow-prod-down_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

6.0ms	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
4.0ms	(/.f64 4 (*.f64 PI.f64 f))
4.0ms	(*.f64 PI.f64 f)
4.0ms	(log.f64 (/.f64 4 (*.f64 PI.f64 f)))

Compiler

Compiled 1324 to 820 computations (38.1% saved)

series328.0ms (1.8%)

Error

0.9b

Counts

4 → 12

Calls

4 calls:

138.0ms	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
115.0ms	(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
38.0ms	(/.f64 4 (*.f64 PI.f64 f))
28.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 325 to 288 computations (11.4% saved)

simplify63.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5068	1423

prune142.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	105	12	117

Error

0.8b

Counts

117 → 12

Compiler

Compiled 1335 to 894 computations (33% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (/.f64 4 f))
0.2b	(+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f)))
0.3b	(/.f64 (+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f))) PI.f64)

rewrite196.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

67×	`*-un-lft-identity_binary64`
45×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
30×	`distribute-lft-out_binary64`
29×	`pow1_binary64` `log-prod_binary64`
26×	`log-pow_binary64`
20×	`distribute-rgt-neg-in_binary64`
13×	`associate-+r+_binary64`
9×	`associate-/l*_binary64`
8×	`add-exp-log_binary64`
5×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`log-div_binary64` `div-inv_binary64` `associate-/r*_binary64` `distribute-neg-in_binary64` `associate-+l+_binary64`
2×	`div-exp_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `div-sub_binary64` `associate-+r-_binary64` `flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64` `sum-log_binary64` `rem-log-exp_binary64`
1×	`cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `neg-log_binary64` `+-commutative_binary64`

Counts

3 → 115

Calls

3 calls:

12.0ms	(+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f)))
10.0ms	(/.f64 (+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f))) PI.f64)
3.0ms	(log.f64 (/.f64 4 f))

Compiler

Compiled 1720 to 1065 computations (38.1% saved)

series413.0ms (2.2%)

Error

0.8b

Counts

3 → 9

Calls

3 calls:

169.0ms	(/.f64 (+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f))) PI.f64)
153.0ms	(+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f)))
80.0ms	(log.f64 (/.f64 4 f))

Compiler

Compiled 341 to 294 computations (13.8% saved)

simplify64.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5003	2236

prune152.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Error

0.8b

Counts

136 → 10

Compiler

Compiled 1464 to 940 computations (35.8% saved)

regimes6.3s (33.5%)

Accuracy

Total 2.2b remaining (83.8%)

Threshold costs 0b (0%)

Compiler

Compiled 72522 to 58148 computations (19.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	35
1	34	35

end2.0ms (0%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

sample7.0s (37.3%)

Algorithm

1×

intervals

Results

2.0s	3937×	body	1024	valid
1.9s	3976×	body	1024	nan
708.0ms	1956×	body	512	valid
661.0ms	1988×	body	512	nan
478.0ms	461×	body	2048	valid
250.0ms	997×	body	256	valid
225.0ms	1003×	body	256	nan
83.0ms	649×	body	128	valid
3.0ms	4×	body	2048	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 294 to 239 computations (18.7% saved)

Details

analyze1.3s (7%)

sample223.0ms (1.2%)

simplify79.0ms (0.4%)

prune10.0ms (0.1%)

localize19.0ms (0.1%)

rewrite622.0ms (3.3%)

series407.0ms (2.2%)

simplify90.0ms (0.5%)

prune363.0ms (1.9%)

localize9.0ms (0%)

rewrite195.0ms (1%)

series392.0ms (2.1%)

simplify58.0ms (0.3%)

prune155.0ms (0.8%)

localize8.0ms (0%)

rewrite162.0ms (0.9%)

series328.0ms (1.8%)

simplify63.0ms (0.3%)

prune142.0ms (0.8%)

localize10.0ms (0.1%)

rewrite196.0ms (1%)

series413.0ms (2.2%)

simplify64.0ms (0.3%)

prune152.0ms (0.8%)

regimes6.3s (33.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end2.0ms (0%)

sample7.0s (37.3%)

Profiling