Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample36.0ms (0.9%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify239.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	5050	41

prune7.0ms (0.2%)

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: 0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 x 4))
0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite55.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_2146`
30×	`associate-r_binary64_2064`
23×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
20×	`times-frac_binary64_2130`
19×	`add-exp-log_binary64_2162`
16×	`add-cbrt-cube_binary64_2160`
13×	`sqrt-prod_binary64_2140`
12×	`pow1_binary64_2185`
9×	`associate-l_binary64_2065`
8×	`prod-exp_binary64_2173`
7×	`unswap-sqr_binary64_2092`
6×	`cbrt-unprod_binary64_2157`
4×	`pow-prod-down_binary64_2195` `unpow-prod-down_binary64_2203` `add-log-exp_binary64_2163`
3×	`*-commutative_binary64_2055`
2×	`sqr-pow_binary64_2096`
1×	`cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `pow-exp_binary64_2192` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `pow-to-exp_binary64_2193` `associate-*r/_binary64_2066` `div-inv_binary64_2121` `div-exp_binary64_2175`

Counts

4 → 99

Calls

4 calls:

23.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
7.0ms	(*.f64 1/5 (pow.f64 x 4))
7.0ms	(.f64 2/3 (.f64 x x))
2.0ms	(sqrt.f64 PI.f64)

series150.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
41.0ms	(*.f64 1/5 (pow.f64 x 4))
32.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 532 to 456 computations (14.3% saved)

simplify96.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4950	2575
1	4950	2575

prune213.0ms (5.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	4	113

Merged error: 0b

Counts

113 → 4

Compiler

Compiled 3962 to 2663 computations (32.8% saved)

localize21.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 6) 1/21)
0.1b	(*.f64 (pow.f64 x 4) 1/5)
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_2146`
19×	`add-exp-log_binary64_2162`
17×	`associate-l_binary64_2065`
13×	`add-cbrt-cube_binary64_2160`
12×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`pow1_binary64_2185`
9×	`prod-exp_binary64_2173`
8×	`unpow-prod-down_binary64_2203`
7×	`unswap-sqr_binary64_2092` `associate-r_binary64_2064`
5×	`cbrt-unprod_binary64_2157`
4×	`add-log-exp_binary64_2163` `sqr-pow_binary64_2096`
3×	`pow-prod-down_binary64_2195` `*-commutative_binary64_2055` `sqrt-prod_binary64_2140`
2×	`pow-exp_binary64_2192` `pow-to-exp_binary64_2193`
1×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`

Counts

4 → 82

Calls

4 calls:

7.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 4) 1/5)
6.0ms	(*.f64 (pow.f64 x 6) 1/21)
1.0ms	(sqrt.f64 PI.f64)

series116.0ms (3%)

Counts

4 → 9

Calls

4 calls:

50.0ms	(*.f64 (pow.f64 x 6) 1/21)
33.0ms	(*.f64 (pow.f64 x 4) 1/5)
32.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 504 to 438 computations (13.1% saved)

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4932	797
1	4932	797

prune152.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	91	4	95

Merged error: 0b

Counts

95 → 4

Compiler

Compiled 3002 to 2091 computations (30.3% saved)

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 2/3 (.f64 x x))
0.5b	(.f64 (sqrt.f64 (.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 (pow.f64 x 4) 1/5)))) (sqrt.f64 PI.f64)))) (sqrt.f64 (.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5)))) (sqrt.f64 PI.f64)))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite65.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`pow1_binary64_2185`
30×	`sqrt-pow1_binary64_2142`
23×	`pow-prod-down_binary64_2195`
16×	`add-sqr-sqrt_binary64_2146`
12×	`pow1/2_binary64_2204`
11×	`add-cube-cbrt_binary64_2159` `add-exp-log_binary64_2162` `*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`
10×	`pow-prod-up_binary64_2194` `sqrt-prod_binary64_2140`
7×	`associate-l_binary64_2065`
6×	`pow-sqr_binary64_2097`
5×	`associate-r/_binary64_2066` `associate-r*_binary64_2064`
4×	`swap-sqr_binary64_2091` `sqrt-div_binary64_2141` `add-log-exp_binary64_2163` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
2×	`unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `rem-sqrt-square_binary64_2137`
1×	`sqrt-unprod_binary64_2144` `associate-*l/_binary64_2067` `pow-plus_binary64_2187` `rem-square-sqrt_binary64_2136` `pow2_binary64_2205` `frac-times_binary64_2134`

Counts

4 → 97

Calls

4 calls:

39.0ms	(.f64 (sqrt.f64 (.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 (pow.f64 x 4) 1/5)))) (sqrt.f64 PI.f64)))) (sqrt.f64 (.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5)))) (sqrt.f64 PI.f64)))))
7.0ms	(.f64 2/3 (.f64 x x))
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series114.0ms (2.9%)

Counts

4 → 9

Calls

4 calls:

80.0ms	(.f64 (sqrt.f64 (.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 (pow.f64 x 4) 1/5)))) (sqrt.f64 PI.f64)))) (sqrt.f64 (.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5)))) (sqrt.f64 PI.f64)))))
33.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 544 to 444 computations (18.4% saved)

simplify81.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4950	2155
1	4950	2155

prune265.0ms (6.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	106	4	110

Merged error: 0b

Counts

110 → 4

Compiler

Compiled 4908 to 3323 computations (32.3% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 6) 1/21)
0.2b	(.f64 2/3 (.f64 x x))
0.3b	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite44.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2146`
19×	`add-exp-log_binary64_2162`
16×	`add-cbrt-cube_binary64_2160`
13×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`pow1_binary64_2185` `associate-l_binary64_2065`
9×	`sqrt-prod_binary64_2140`
7×	`prod-exp_binary64_2173`
6×	`associate-/r*_binary64_2068` `times-frac_binary64_2130`
5×	`cbrt-unprod_binary64_2157`
4×	`unswap-sqr_binary64_2092` `unpow-prod-down_binary64_2203` `add-log-exp_binary64_2163` `associate-r_binary64_2064`
3×	`pow-prod-down_binary64_2195`
2×	`cbrt-undiv_binary64_2158` `-commutative_binary64_2055` `sqr-pow_binary64_2096` `associate-r/_binary64_2066` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `pow-exp_binary64_2192` `associate-/l*_binary64_2069` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `pow-to-exp_binary64_2193` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 86

Calls

4 calls:

18.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
9.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 6) 1/21)
1.0ms	(sqrt.f64 PI.f64)

series150.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
45.0ms	(*.f64 (pow.f64 x 6) 1/21)
31.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 532 to 456 computations (14.3% saved)

simplify49.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4943	1939
1	4943	1939

prune149.0ms (3.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	98	4	102

Merged error: 0b

Counts

102 → 4

Compiler

Compiled 2975 to 1996 computations (32.9% saved)

regimes263.0ms (6.7%)

Compiler: Compiled 3265 to 2328 computations (28.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	41
1	30	41

end0.0ms (0%)

sample1.5s (37.9%)

Algorithm

1×

intervals

Results

736.0ms	8000×	body	128	valid
100.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 654 to 477 computations (27.1% saved)

Details

analyze6.0ms (0.2%)

sample36.0ms (0.9%)

simplify239.0ms (6.1%)

prune7.0ms (0.2%)

localize18.0ms (0.5%)

rewrite55.0ms (1.4%)

series150.0ms (3.8%)

simplify96.0ms (2.5%)

prune213.0ms (5.5%)

localize21.0ms (0.6%)

rewrite29.0ms (0.8%)

series116.0ms (3%)

simplify59.0ms (1.5%)

prune152.0ms (3.9%)

localize24.0ms (0.6%)

rewrite65.0ms (1.7%)

series114.0ms (2.9%)

simplify81.0ms (2.1%)

prune265.0ms (6.8%)

localize18.0ms (0.5%)

rewrite44.0ms (1.1%)

series150.0ms (3.9%)

simplify49.0ms (1.3%)

prune149.0ms (3.8%)

regimes263.0ms (6.7%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (37.9%)

Profiling