Details

analyze198.0ms (0.7%)

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)

sample28.0ms (0.1%)

Algorithm

1×

intervals

Results

18.0ms

256×

body

128

valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify210.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4990	40
1	4990	40

prune14.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.4b

Counts

2 → 2

Compiler

Compiled 80 to 61 computations (23.8% saved)

localize43.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.3b	(*.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))))))

rewrite80.0ms (0.3%)

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:

22.0ms	(/.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))))
14.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
12.0ms	(.f64 3 (.f64 v v))
7.0ms	(*.f64 PI.f64 t)

series408.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.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))))
155.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
27.0ms	(.f64 3 (.f64 v v))
13.0ms	(*.f64 PI.f64 t)

simplify107.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5172	2803

prune760.0ms (2.5%)

Pruning

40 alts after pruning (39 fresh and 1 done)

	Pruned	Kept	Total
New	68	38	106
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	68	40	108

Merged error: 0.1b

Counts

108 → 40

Compiler

Compiled 5308 to 3419 computations (35.6% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite106.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64_2162`
28×	`add-cbrt-cube_binary64_2160`
18×	`associate-*r/_binary64_2066`
16×	`pow1_binary64_2185`
15×	`add-sqr-sqrt_binary64_2146`
13×	`prod-exp_binary64_2173` `associate-r_binary64_2064` `cbrt-unprod_binary64_2157`
11×	`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`
7×	`pow-prod-down_binary64_2195`
5×	`associate-l_binary64_2065`
4×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `cbrt-prod_binary64_2155` `frac-times_binary64_2134` `div-exp_binary64_2175`
3×	`unswap-sqr_binary64_2092` `associate-/l_binary64_2069` `-commutative_binary64_2055` `times-frac_binary64_2130`
2×	`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 → 98

Calls

4 calls:

35.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 v v) (cbrt.f64 3))))))) (-.f64 1 (*.f64 v v))))
23.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (*.f64 v v) (cbrt.f64 3)))))))
14.0ms	(.f64 (.f64 v v) (cbrt.f64 3))
7.0ms	(*.f64 PI.f64 t)

series891.0ms (3%)

Counts

4 → 12

Calls

4 calls:

579.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 v v) (cbrt.f64 3))))))) (-.f64 1 (*.f64 v v))))
238.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (*.f64 v v) (cbrt.f64 3)))))))
55.0ms	(.f64 (.f64 v v) (cbrt.f64 3))
18.0ms	(*.f64 PI.f64 t)

simplify161.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5190	2966

prune1.2s (4.1%)

Pruning

58 alts after pruning (56 fresh and 2 done)

	Pruned	Kept	Total
New	87	23	110
Fresh	5	33	38
Picked	0	1	1
Done	0	1	1
Total	92	58	150

Merged error: 0.1b

Counts

150 → 58

Compiler

Compiled 6952 to 4796 computations (31% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v))) (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v))))))))) (-.f64 1 (.f64 v v))))
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v))) (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v)))))))))
30.9b	(sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v)))
30.9b	(sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v)))

rewrite102.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
21×	`pow1_binary64_2185`
18×	`associate-*r/_binary64_2066`
9×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
8×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `sqrt-div_binary64_2141`
7×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
6×	`sqrt-pow1_binary64_2142`
4×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `associate-r_binary64_2064` `frac-times_binary64_2134` `div-exp_binary64_2175`
3×	`associate-/l*_binary64_2069` `sqrt-prod_binary64_2140` `times-frac_binary64_2130`
2×	`associate-*l/_binary64_2067` `pow1/2_binary64_2204` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `-commutative_binary64_2055` `associate-/r_binary64_2068` `associate-l_binary64_2065` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 81

Calls

4 calls:

33.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v))) (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v))))))))) (-.f64 1 (.f64 v v))))
23.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v))) (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v)))))))))
10.0ms	(sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v)))
7.0ms	(sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v)))

series935.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

540.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v))) (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v))))))))) (-.f64 1 (.f64 v v))))
269.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v))) (sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v)))))))))
65.0ms	(sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v)))
61.0ms	(sqrt.f64 (.f64 (cbrt.f64 3) (.f64 v v)))

simplify86.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4997	2828
1	4997	2828

prune1.5s (5%)

Pruning

69 alts after pruning (66 fresh and 3 done)

	Pruned	Kept	Total
New	78	15	93
Fresh	4	51	55
Picked	0	1	1
Done	0	2	2
Total	82	69	151

Merged error: 0.1b

Counts

151 → 69

Compiler

Compiled 7552 to 5287 computations (30% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.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 (cbrt.f64 (.f64 (pow.f64 v 6) 27)))))) (-.f64 1 (.f64 v v))))
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 27))))))
18.8b	(cbrt.f64 (*.f64 (pow.f64 v 6) 27))

rewrite49.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
18×	`associate-*r/_binary64_2066`
11×	`pow1_binary64_2185` `add-sqr-sqrt_binary64_2146`
10×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
9×	`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`
7×	`associate-r_binary64_2064`
4×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `associate-l_binary64_2065` `frac-times_binary64_2134` `div-exp_binary64_2175`
3×	`associate-/l*_binary64_2069` `times-frac_binary64_2130`
2×	`-commutative_binary64_2055` `associate-l/_binary64_2067` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `unswap-sqr_binary64_2092` `sqrt-prod_binary64_2140` `associate-/r*_binary64_2068` `pow1/3_binary64_2206` `cbrt-prod_binary64_2155` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 84

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 (cbrt.f64 (.f64 (pow.f64 v 6) 27)))))) (-.f64 1 (.f64 v v))))
13.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 27))))))
4.0ms	(*.f64 PI.f64 t)
4.0ms	(cbrt.f64 (*.f64 (pow.f64 v 6) 27))

series319.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 27)))))) (-.f64 1 (.f64 v v))))
91.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (cbrt.f64 (.f64 (pow.f64 v 6) 27))))))
19.0ms	(cbrt.f64 (*.f64 (pow.f64 v 6) 27))
16.0ms	(*.f64 PI.f64 t)

simplify88.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4977	2889
1	4977	2889

prune1.9s (6.3%)

Pruning

93 alts after pruning (89 fresh and 4 done)

	Pruned	Kept	Total
New	69	27	96
Fresh	3	62	65
Picked	0	1	1
Done	0	3	3
Total	72	93	165

Merged error: 0.1b

Counts

165 → 93

Compiler

Compiled 3547 to 2420 computations (31.8% saved)

regimes4.5s (14.9%)

Compiler: Compiled 51055 to 39714 computations (22.2% saved)

bsearch3.9s (12.8%)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	50
1	90	50

end0.0ms (0%)

sample12.5s (41.4%)

Algorithm

1×

intervals

Results

713.0ms	8000×	body	128	valid
1.0ms	15×	body	128	nan

Compiler

Compiled 9404 to 7336 computations (22% saved)

Pareto

Details

analyze198.0ms (0.7%)

sample28.0ms (0.1%)

simplify210.0ms (0.7%)

prune14.0ms (0%)

localize43.0ms (0.1%)

rewrite80.0ms (0.3%)

series408.0ms (1.4%)

simplify107.0ms (0.4%)

prune760.0ms (2.5%)

localize25.0ms (0.1%)

rewrite106.0ms (0.4%)

series891.0ms (3%)

simplify161.0ms (0.5%)

prune1.2s (4.1%)

localize22.0ms (0.1%)

rewrite102.0ms (0.3%)

series935.0ms (3.1%)

simplify86.0ms (0.3%)

prune1.5s (5%)

localize19.0ms (0.1%)

rewrite49.0ms (0.2%)

series319.0ms (1.1%)

simplify88.0ms (0.3%)

prune1.9s (6.3%)

regimes4.5s (14.9%)

bsearch3.9s (12.8%)

simplify7.0ms (0%)

end0.0ms (0%)

sample12.5s (41.4%)

Profiling