Details

analyze104.0ms (1.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify143.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4990	40
1	4990	40

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.4b

Counts

2 → 1

Compiler

Compiled 54 to 41 computations (24.1% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
18×	`associate-*r/_binary64_2066`
16×	`pow1_binary64_2185`
13×	`prod-exp_binary64_2173` `add-sqr-sqrt_binary64_2146` `cbrt-unprod_binary64_2157`
10×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
8×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `sqrt-div_binary64_2141` `associate-r_binary64_2064`
7×	`pow-prod-down_binary64_2195` `associate-l_binary64_2065`
4×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `frac-times_binary64_2134` `div-exp_binary64_2175`
3×	`associate-/l_binary64_2069` `-commutative_binary64_2055` `times-frac_binary64_2130`
2×	`unswap-sqr_binary64_2092` `associate-*l/_binary64_2067` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `sqrt-prod_binary64_2140` `associate-/r*_binary64_2068` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 94

Calls

4 calls:

17.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
10.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
6.0ms	(.f64 3 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

series313.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
101.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
17.0ms	(.f64 3 (.f64 v v))
13.0ms	(*.f64 PI.f64 t)

simplify59.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5172	2803

prune207.0ms (3.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Error

0.1b

Counts

107 → 10

Compiler

Compiled 4155 to 2579 computations (37.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
0.3b	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
0.4b	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))

rewrite54.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`associate-*r/_binary64_2066` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
16×	`pow1_binary64_2185`
13×	`prod-exp_binary64_2173` `add-sqr-sqrt_binary64_2146` `cbrt-unprod_binary64_2157`
10×	`sqrt-div_binary64_2141` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-l_binary64_2065`
8×	`associate-/r/_binary64_2070`
7×	`pow-prod-down_binary64_2195`
6×	`associate-r_binary64_2064`
4×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `frac-times_binary64_2134` `div-exp_binary64_2175`
3×	`associate-/l_binary64_2069` `-commutative_binary64_2055` `times-frac_binary64_2130`
2×	`unswap-sqr_binary64_2092` `associate-*l/_binary64_2067` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `sqrt-prod_binary64_2140` `associate-/r*_binary64_2068` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 96

Calls

4 calls:

16.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
10.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
8.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
6.0ms	(.f64 3 (.f64 v v))

series374.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
98.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
82.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
20.0ms	(.f64 3 (.f64 v v))

simplify59.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5227	3124

prune198.0ms (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	108	10	118

Error

0.1b

Counts

118 → 10

Compiler

Compiled 4222 to 2747 computations (34.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
8.8b	(/.f64 (.f64 (.f64 v v) 5) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))

rewrite82.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_2162`
82×	`add-cbrt-cube_binary64_2160`
54×	`prod-exp_binary64_2173`
42×	`cbrt-unprod_binary64_2157`
36×	`associate-*r/_binary64_2066`
24×	`pow1_binary64_2185`
20×	`div-exp_binary64_2175`
16×	`cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `sqrt-div_binary64_2141`
14×	`flip--_binary64_2099` `flip3--_binary64_2128`
12×	`pow-prod-down_binary64_2195`
8×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `associate-r_binary64_2064` `frac-times_binary64_2134` `*-un-lft-identity_binary64_2124`
4×	`associate-/l_binary64_2069` `add-log-exp_binary64_2163` `associate-l/_binary64_2067` `pow-flip_binary64_2198` `1-exp_binary64_2168` `times-frac_binary64_2130` `rec-exp_binary64_2174`
2×	`clear-num_binary64_2123` `-commutative_binary64_2055` `sqrt-prod_binary64_2140` `associate-/r_binary64_2068` `associate-l_binary64_2065` `div-inv_binary64_2121` `frac-2neg_binary64_2135`
1×	`inv-pow_binary64_2209`

Counts

4 → 133

Calls

4 calls:

24.0ms	(/.f64 (.f64 (.f64 v v) 5) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
15.0ms	(/.f64 1 (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
10.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
10.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

series567.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(/.f64 1 (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
176.0ms	(/.f64 (.f64 (.f64 v v) 5) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
94.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
86.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

simplify86.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4950	4883
1	4950	4883

prune426.0ms (7.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	146	9	155

Error

0.1b

Counts

155 → 9

Compiler

Compiled 8476 to 5109 computations (39.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 2)) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))))
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 2))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
17×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
16×	`pow1_binary64_2185`
14×	`add-sqr-sqrt_binary64_2146`
11×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`associate-r_binary64_2064`
8×	`associate-/r/_binary64_2070` `associate-*r/_binary64_2066`
7×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `associate-l_binary64_2065`
6×	`sqrt-div_binary64_2141`
5×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
4×	`add-log-exp_binary64_2163` `frac-times_binary64_2134`
3×	`associate-/l_binary64_2069` `-commutative_binary64_2055` `sqrt-prod_binary64_2140` `times-frac_binary64_2130`
2×	`unswap-sqr_binary64_2092` `associate-*l/_binary64_2067` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `associate-/r*_binary64_2068` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 96

Calls

4 calls:

18.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 2)) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))))
9.0ms	(.f64 3 (.f64 v v))
6.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 2))
4.0ms	(*.f64 PI.f64 t)

series248.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

179.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 2)) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v))))
38.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 2))
16.0ms	(.f64 3 (.f64 v v))
14.0ms	(*.f64 PI.f64 t)

simplify91.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4949	2671
1	4949	2671

prune167.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	109	8	117

Error

0.1b

Counts

117 → 8

Compiler

Compiled 3797 to 2347 computations (38.2% saved)

regimes476.0ms (8.7%)

Accuracy

Total 0.3b remaining (67.2%)

Threshold costs 0.3b (67.2%)

Compiler

Compiled 7790 to 5679 computations (27.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	43
1	80	43

end0.0ms (0%)

sample1.6s (29.3%)

Algorithm

1×

intervals

Results

513.0ms	8000×	body	128	valid
0.0ms	8×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 1400 to 1022 computations (27% saved)

Details

analyze104.0ms (1.9%)

sample25.0ms (0.5%)

simplify143.0ms (2.6%)

prune4.0ms (0.1%)

localize21.0ms (0.4%)

rewrite48.0ms (0.9%)

series313.0ms (5.7%)

simplify59.0ms (1.1%)

prune207.0ms (3.8%)

localize15.0ms (0.3%)

rewrite54.0ms (1%)

series374.0ms (6.9%)

simplify59.0ms (1.1%)

prune198.0ms (3.6%)

localize17.0ms (0.3%)

rewrite82.0ms (1.5%)

series567.0ms (10.4%)

simplify86.0ms (1.6%)

prune426.0ms (7.8%)

localize16.0ms (0.3%)

rewrite48.0ms (0.9%)

series248.0ms (4.5%)

simplify91.0ms (1.7%)

prune167.0ms (3.1%)

regimes476.0ms (8.7%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (29.3%)

Profiling