Details

analyze2.1s (7.3%)

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)

sample457.0ms (1.6%)

Algorithm

1×

intervals

Results

120.0ms	119×	body	1024	nan
117.0ms	115×	body	1024	valid
51.0ms	74×	body	512	nan
46.0ms	63×	body	512	valid
40.0ms	19×	body	2048	valid
19.0ms	38×	body	256	valid
14.0ms	30×	body	256	nan
5.0ms	21×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify323.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	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

Error

61.4b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize50.0ms (0.2%)

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))))
7.2b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite805.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

61.3b

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:

26.0ms	(/.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))))
15.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
14.0ms	(*.f64 (/.f64 PI.f64 4) f)
13.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 6543 to 4377 computations (33.1% saved)

series492.0ms (1.7%)

Error

1.5b

Counts

4 → 12

Calls

4 calls:

245.0ms	(/.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))))
97.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
56.0ms	(*.f64 (/.f64 PI.f64 4) f)
53.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1240 to 921 computations (25.7% saved)

simplify178.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5172	5387

prune664.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	149	5	154

Error

1.5b

Counts

154 → 5

Compiler

Compiled 6707 to 4500 computations (32.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
0.2b	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
0.2b	(.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))

rewrite264.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

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:

21.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
11.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
10.0ms	(.f64 f (.f64 PI.f64 1/2))
10.0ms	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))

Compiler

Compiled 1805 to 1377 computations (23.7% saved)

series447.0ms (1.6%)

Error

1.3b

Counts

4 → 12

Calls

4 calls:

192.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
131.0ms	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
53.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
48.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 420 to 356 computations (15.2% saved)

simplify122.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5045	1497

prune233.0ms (0.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	93	13	106
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	94	17	111

Error

1.1b

Counts

111 → 17

Compiler

Compiled 1967 to 1402 computations (28.7% saved)

localize25.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b	(+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64)))
0.4b	(*.f64 (+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64))) (/.f64 -4 PI.f64))
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite264.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

40×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
29×	`log-prod_binary64`
28×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
16×	`pow1_binary64`
13×	`associate-r_binary64` `associate-+r+_binary64`
12×	`distribute-lft-out_binary64`
11×	`log-pow_binary64` `add-exp-log_binary64`
9×	`associate-l_binary64`
8×	`add-cbrt-cube_binary64` `distribute-rgt-neg-in_binary64`
4×	`add-log-exp_binary64`
3×	`div-inv_binary64` `flip3-+_binary64` `flip-+_binary64` `distribute-neg-in_binary64` `associate-+l+_binary64`
2×	`log-div_binary64` `div-exp_binary64` `rem-log-exp_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `unswap-sqr_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `-commutative_binary64` `neg-log_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `associate-+r-_binary64` `+-commutative_binary64`

Counts

3 → 102

Calls

3 calls:

26.0ms	(*.f64 (+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64))) (/.f64 -4 PI.f64))
18.0ms	(+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64)))
5.0ms	(log.f64 (/.f64 4 PI.f64))

Compiler

Compiled 2054 to 1298 computations (36.8% saved)

series434.0ms (1.5%)

Error

1.1b

Counts

3 → 6

Calls

3 calls:

237.0ms	(*.f64 (+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64))) (/.f64 -4 PI.f64))
182.0ms	(+.f64 (neg.f64 (log.f64 f)) (log.f64 (/.f64 4 PI.f64)))
0.0ms	(log.f64 (/.f64 4 PI.f64))

Compiler

Compiled 240 to 211 computations (12.1% saved)

simplify136.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5237	1939

prune241.0ms (0.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	108	17	125

Error

1.1b

Counts

125 → 17

Compiler

Compiled 2260 to 1545 computations (31.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (.f64 1/2 (.f64 PI.f64 f)))
0.2b	(-.f64 (log.f64 2) (log.f64 (.f64 1/2 (.f64 PI.f64 f))))
0.2b	(*.f64 PI.f64 f)
0.4b	(.f64 (-.f64 (log.f64 2) (log.f64 (.f64 1/2 (*.f64 PI.f64 f)))) (/.f64 -4 PI.f64))

rewrite288.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

52×	`pow1_binary64`
28×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`log-pow_binary64`
20×	`pow-prod-down_binary64`
17×	`add-exp-log_binary64`
16×	`add-cube-cbrt_binary64` `distribute-lft-out--_binary64` `associate-r_binary64`
15×	`associate-l_binary64`
11×	`add-cbrt-cube_binary64`
10×	`times-frac_binary64`
6×	`prod-exp_binary64` `cancel-sign-sub-inv_binary64`
5×	`log-prod_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `flip3--_binary64` `flip--_binary64` `unswap-sqr_binary64` `associate--l+_binary64` `rem-log-exp_binary64`
2×	`frac-times_binary64` `associate-l/_binary64` `difference-of-squares_binary64` `-commutative_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `div-inv_binary64` `diff-log_binary64` `sub-neg_binary64` `associate--r+_binary64`

Counts

4 → 107

Calls

4 calls:

34.0ms	(.f64 (-.f64 (log.f64 2) (log.f64 (.f64 1/2 (*.f64 PI.f64 f)))) (/.f64 -4 PI.f64))
16.0ms	(-.f64 (log.f64 2) (log.f64 (.f64 1/2 (.f64 PI.f64 f))))
8.0ms	(log.f64 (.f64 1/2 (.f64 PI.f64 f)))
7.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 2200 to 1560 computations (29.1% saved)

series636.0ms (2.2%)

Error

1.1b

Counts

4 → 12

Calls

4 calls:

247.0ms	(.f64 (-.f64 (log.f64 2) (log.f64 (.f64 1/2 (*.f64 PI.f64 f)))) (/.f64 -4 PI.f64))
206.0ms	(-.f64 (log.f64 2) (log.f64 (.f64 1/2 (.f64 PI.f64 f))))
128.0ms	(log.f64 (.f64 1/2 (.f64 PI.f64 f)))
37.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 531 to 469 computations (11.7% saved)

simplify141.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5002	2199

prune214.0ms (0.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	4	11	15
Picked	1	0	1
Done	0	1	1
Total	121	15	136

Error

1.1b

Counts

136 → 15

Compiler

Compiled 2163 to 1642 computations (24.1% saved)

regimes1.9s (6.8%)

Accuracy

Total 1.1b remaining (41.7%)

Threshold costs 0b (0%)

Compiler

Compiled 13752 to 11198 computations (18.6% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	20
1	15	20

end0.0ms (0%)

sample18.2s (63.4%)

Algorithm

1×

intervals

Results

4.1s	3915×	body	1024	valid
3.8s	3947×	body	1024	nan
1.5s	1954×	body	512	valid
1.4s	1984×	body	512	nan
1.0s	510×	body	2048	valid
505.0ms	1001×	body	256	valid
466.0ms	1012×	body	256	nan
166.0ms	620×	body	128	valid
4.0ms	3×	body	2048	nan
0.0ms	2×	body	128	overflowed
0.0ms	1×	body	128	nan

Compiler

Compiled 2296 to 1872 computations (18.5% saved)

Details

analyze2.1s (7.3%)

sample457.0ms (1.6%)

simplify323.0ms (1.1%)

prune14.0ms (0.1%)

localize50.0ms (0.2%)

rewrite805.0ms (2.8%)

series492.0ms (1.7%)

simplify178.0ms (0.6%)

prune664.0ms (2.3%)

localize18.0ms (0.1%)

rewrite264.0ms (0.9%)

series447.0ms (1.6%)

simplify122.0ms (0.4%)

prune233.0ms (0.8%)

localize25.0ms (0.1%)

rewrite264.0ms (0.9%)

series434.0ms (1.5%)

simplify136.0ms (0.5%)

prune241.0ms (0.8%)

localize22.0ms (0.1%)

rewrite288.0ms (1%)

series636.0ms (2.2%)

simplify141.0ms (0.5%)

prune214.0ms (0.7%)

regimes1.9s (6.8%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample18.2s (63.4%)

Profiling