Details

analyze108.0ms (1.7%)

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)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify143.0ms (2.2%)

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

0.6b

Counts

2 → 1

Compiler

Compiled 54 to 41 computations (24.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.3b	(*.f64 PI.f64 t)
0.5b	(/.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))))
0.5b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

rewrite52.0ms (0.8%)

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:

18.0ms	(/.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))))
11.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
7.0ms	(*.f64 PI.f64 t)
6.0ms	(.f64 3 (.f64 v v))

series294.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(/.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))))
93.0ms	(.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)

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5172	2803

prune191.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	98	8	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	9	107

Error

0.3b

Counts

107 → 9

Compiler

Compiled 4082 to 2525 computations (38.1% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.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))))))
0.5b	(/.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))))

rewrite53.0ms (0.8%)

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:

17.0ms	(/.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)))))))
9.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
6.0ms	(.f64 3 (.f64 v v))

series361.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(/.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))))
87.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
84.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
16.0ms	(.f64 3 (.f64 v v))

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5227	3124

prune199.0ms (3.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	106	11	117

Error

0.3b

Counts

117 → 11

Compiler

Compiled 4281 to 2791 computations (34.8% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 t)
0.3b	(.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))
0.4b	(.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))

rewrite142.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

368×	`associate-*r/_binary64_2066`
228×	`cbrt-div_binary64_2156` `sqrt-div_binary64_2141`
168×	`frac-times_binary64_2134`
142×	`flip--_binary64_2099` `flip3--_binary64_2128`
84×	`associate-*l/_binary64_2067`
80×	`associate-/r/_binary64_2070`
69×	`add-exp-log_binary64_2162`
47×	`add-cbrt-cube_binary64_2160`
41×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
36×	`pow1_binary64_2185`
22×	`pow-prod-down_binary64_2195`
12×	`add-sqr-sqrt_binary64_2146`
11×	`associate-r_binary64_2064`
10×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
7×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
5×	`associate-l_binary64_2065`
4×	`add-log-exp_binary64_2163` `cbrt-prod_binary64_2155`
3×	`associate-/l_binary64_2069` `-commutative_binary64_2055` `times-frac_binary64_2130`
2×	`associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `unswap-sqr_binary64_2092` `sqrt-prod_binary64_2140` `associate-/r*_binary64_2068` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 219

Calls

4 calls:

38.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
19.0ms	(.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
13.0ms	(.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))
4.0ms	(*.f64 PI.f64 t)

series518.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))))
184.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
102.0ms	(.f64 (.f64 (.f64 PI.f64 t) (.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
13.0ms	(*.f64 PI.f64 t)

simplify133.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5004	13158

prune1.0s (16.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	3	5	8
Picked	0	1	1
Done	0	2	2
Total	231	11	242

Error

0.3b

Counts

242 → 11

Compiler

Compiled 16148 to 11087 computations (31.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 t (.f64 PI.f64 (sqrt.f64 2)))
0.5b	(/.f64 1 (.f64 t (.f64 PI.f64 (sqrt.f64 2))))
2.3b	(/.f64 (pow.f64 v 4) (.f64 t (.f64 PI.f64 (sqrt.f64 2))))
5.9b	(/.f64 (.f64 v v) (.f64 t (*.f64 PI.f64 (sqrt.f64 2))))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-exp-log_binary64_2162`
48×	`add-cbrt-cube_binary64_2160`
30×	`prod-exp_binary64_2173`
21×	`div-exp_binary64_2175`
18×	`cbrt-unprod_binary64_2157`
15×	`pow1_binary64_2185`
12×	`cbrt-undiv_binary64_2158`
11×	`associate-/l_binary64_2069` `add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `times-frac_binary64_2130` `-un-lft-identity_binary64_2124`
6×	`pow-prod-down_binary64_2195` `unpow-prod-down_binary64_2203`
4×	`add-log-exp_binary64_2163`
3×	`clear-num_binary64_2123` `pow-exp_binary64_2192` `associate-/r_binary64_2068` `associate-l*_binary64_2065` `pow-flip_binary64_2198` `pow-to-exp_binary64_2193` `1-exp_binary64_2168` `div-inv_binary64_2121` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
2×	`sqr-pow_binary64_2096`
1×	`-commutative_binary64_2055` `associate-r*_binary64_2064` `inv-pow_binary64_2209`

Counts

4 → 113

Calls

4 calls:

9.0ms	(/.f64 (.f64 v v) (.f64 t (*.f64 PI.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (pow.f64 v 4) (.f64 t (.f64 PI.f64 (sqrt.f64 2))))
7.0ms	(/.f64 1 (.f64 t (.f64 PI.f64 (sqrt.f64 2))))
6.0ms	(.f64 t (.f64 PI.f64 (sqrt.f64 2)))

series184.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(/.f64 (.f64 v v) (.f64 t (*.f64 PI.f64 (sqrt.f64 2))))
49.0ms	(/.f64 (pow.f64 v 4) (.f64 t (.f64 PI.f64 (sqrt.f64 2))))
48.0ms	(/.f64 1 (.f64 t (.f64 PI.f64 (sqrt.f64 2))))
34.0ms	(.f64 t (.f64 PI.f64 (sqrt.f64 2)))

simplify108.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4958	1940
1	4958	1940

prune242.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	4	3	7
Picked	0	1	1
Done	2	1	3
Total	129	7	136

Error

0.0b

Counts

136 → 7

Compiler

Compiled 4641 to 3318 computations (28.5% saved)

regimes565.0ms (8.9%)

Accuracy

Total 0.5b remaining (96%)

Threshold costs 0.5b (96%)

Compiler

Compiled 9389 to 6968 computations (25.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	107	55
1	107	55

end0.0ms (0%)

sample1.8s (27.8%)

Algorithm

1×

intervals

Results

521.0ms	8000×	body	128	valid
1.0ms	9×	body	128	nan

Compiler

Compiled 1537 to 1149 computations (25.2% saved)

Details

analyze108.0ms (1.7%)

sample24.0ms (0.4%)

simplify143.0ms (2.2%)

prune4.0ms (0.1%)

localize16.0ms (0.2%)

rewrite52.0ms (0.8%)

series294.0ms (4.6%)

simplify62.0ms (1%)

prune191.0ms (3%)

localize16.0ms (0.3%)

rewrite53.0ms (0.8%)

series361.0ms (5.7%)

simplify62.0ms (1%)

prune199.0ms (3.1%)

localize21.0ms (0.3%)

rewrite142.0ms (2.2%)

series518.0ms (8.1%)

simplify133.0ms (2.1%)

prune1.0s (16.4%)

localize16.0ms (0.3%)

rewrite45.0ms (0.7%)

series184.0ms (2.9%)

simplify108.0ms (1.7%)

prune242.0ms (3.8%)

regimes565.0ms (8.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (27.8%)

Profiling