Details

analyze1.1s (3.7%)

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)

sample222.0ms (0.8%)

Algorithm

1×

intervals

Results

63.0ms	136×	body	1024	nan
62.0ms	120×	body	1024	valid
29.0ms	73×	body	512	valid
21.0ms	62×	body	512	nan
14.0ms	13×	body	2048	valid
9.0ms	35×	body	256	valid
7.0ms	31×	body	256	nan
2.0ms	15×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify170.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune8.0ms (0%)

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: 62.2b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize24.0ms (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)
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))))
5.4b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite55.0ms (0.2%)

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:

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)

series366.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

272.0ms	(/.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))))
58.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
18.0ms	(*.f64 (/.f64 PI.f64 4) f)
18.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5184	5751

prune435.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	4	154

Merged error: 1.9b

Counts

154 → 4

Compiler

Compiled 7071 to 4789 computations (32.3% saved)

localize88.0ms (0.3%)

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)

rewrite34.0ms (0.1%)

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:

2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 3)
2.0ms	(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 4)
0.0ms	(pow.f64 PI.f64 3)

simplify39.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5373	1148

prune1.1s (3.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	78	4	82

Merged error: 1.9b

Counts

82 → 4

Compiler

Compiled 14091 to 11062 computations (21.5% saved)

localize97.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))

rewrite56.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`cbrt-prod_binary64`
16×	`unpow-prod-down_binary64`
13×	`pow1_binary64`
12×	`pow-unpow_binary64`
10×	`add-exp-log_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `pow1/3_binary64` `associate-l_binary64` `pow-exp_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`pow-pow_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
5.0ms	(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
0.0ms	(pow.f64 PI.f64 4)

simplify68.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5185	1176

prune1.8s (6.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Merged error: 1.9b

Counts

108 → 4

Compiler

Compiled 19719 to 15696 computations (20.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
1.0b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
1.2b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))))
5.3b	(-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2)))

rewrite354.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

1200×	`times-frac_binary64`
1047×	`*-un-lft-identity_binary64`
947×	`add-sqr-sqrt_binary64`
504×	`difference-of-squares_binary64`
359×	`add-cube-cbrt_binary64`
302×	`distribute-lft-out_binary64`
297×	`unpow-prod-down_binary64`
295×	`sqr-pow_binary64`
285×	`log-prod_binary64`
126×	`unpow-prod-up_binary64`
74×	`associate-/r*_binary64`
42×	`distribute-lft-out--_binary64`
22×	`associate-/r/_binary64`
20×	`associate-/l*_binary64`
17×	`add-exp-log_binary64`
12×	`div-inv_binary64`
11×	`flip3-+_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
7×	`cancel-sign-sub-inv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64`
3×	`rem-log-exp_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `div-sub_binary64` `log-div_binary64`

Counts

4 → 800

Calls

4 calls:

42.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))))
33.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
26.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
11.0ms	(-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2)))

series2.9s (9.8%)

Counts

4 → 12

Calls

4 calls:

2.2s	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))))
447.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
193.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
69.0ms	(-.f64 (pow.f64 (exp.f64 (/.f64 PI.f64 4)) (+.f64 f f)) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2)))

simplify813.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

812 → 812

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5052	104297

prune8.5s (28.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	811	1	812
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	811	5	816

Merged error: 1.7b

Counts

816 → 5

Compiler

Compiled 71544 to 47388 computations (33.8% saved)

regimes1.0s (3.5%)

Compiler: Compiled 18504 to 14222 computations (23.1% saved)

bsearch0.0ms (0%)

simplify73.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	2064	1998
1	2064	1998

end0.0ms (0%)

sample9.8s (33.7%)

Algorithm

1×

intervals

Results

1.9s	3922×	body	1024	valid
1.8s	3972×	body	1024	nan
703.0ms	2001×	body	512	valid
647.0ms	1988×	body	512	nan
491.0ms	474×	body	2048	valid
234.0ms	966×	body	256	valid
214.0ms	974×	body	256	nan
83.0ms	637×	body	128	valid
5.0ms	7×	body	2048	nan
0.0ms	4×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 4291 to 3281 computations (23.5% saved)

Details

analyze1.1s (3.7%)

sample222.0ms (0.8%)

simplify170.0ms (0.6%)

prune8.0ms (0%)

localize24.0ms (0.1%)

rewrite55.0ms (0.2%)

series366.0ms (1.3%)

simplify80.0ms (0.3%)

prune435.0ms (1.5%)

localize88.0ms (0.3%)

rewrite34.0ms (0.1%)

series0.0ms (0%)

simplify39.0ms (0.1%)

prune1.1s (3.9%)

localize97.0ms (0.3%)

rewrite56.0ms (0.2%)

series0.0ms (0%)

simplify68.0ms (0.2%)

prune1.8s (6.3%)

localize25.0ms (0.1%)

rewrite354.0ms (1.2%)

series2.9s (9.8%)

simplify813.0ms (2.8%)

prune8.5s (28.9%)

regimes1.0s (3.5%)

bsearch0.0ms (0%)

simplify73.0ms (0.2%)

end0.0ms (0%)

sample9.8s (33.7%)

Profiling