Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample77.0ms (0.8%)

Algorithm

1×

intervals

Results

60.0ms	256×	body	128	valid
4.0ms	259×	pre	128	true
1.0ms	3×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify175.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5512	47

prune9.0ms (0.1%)

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

Error

2.3b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.4b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
1.0b	(sqrt.f64 PI.f64)
2.3b	(exp.f64 (*.f64 x x))

rewrite96.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`times-frac_binary64_2130`
84×	`add-sqr-sqrt_binary64_2146`
79×	`*-un-lft-identity_binary64_2124`
70×	`add-cube-cbrt_binary64_2159` `associate-l_binary64_2065`
31×	`sqrt-prod_binary64_2140`
18×	`add-cbrt-cube_binary64_2160`
17×	`add-exp-log_binary64_2162`
7×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163`
5×	`cbrt-undiv_binary64_2158` `distribute-lft-out_binary64_2075` `associate-r_binary64_2064` `div-inv_binary64_2121` `div-exp_binary64_2175`
4×	`unswap-sqr_binary64_2092` `associate-/l*_binary64_2069` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`associate-*r/_binary64_2066` `frac-times_binary64_2134` `associate-/l/_binary64_2071`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `exp-to-pow_binary64_2186` `associate-/r_binary64_2068` `rem-sqrt-square_binary64_2137` `associate-*l/_binary64_2067` `rem-exp-log_binary64_2164` `pow1/2_binary64_2204` `distribute-rgt-in_binary64_2074` `exp-prod_binary64_2176` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 149

Calls

4 calls:

57.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
11.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

series158.0ms (1.7%)

Counts

4 → 10

Calls

4 calls:

98.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
51.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
8.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify124.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4944	6254
1	4944	6254

prune369.0ms (4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	137	22	159
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	139	22	161

Error

0.3b

Counts

161 → 22

Compiler

Compiled 7863 to 3663 computations (53.4% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.0b	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0b	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
1.0b	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2146`
28×	`pow1_binary64_2185`
22×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
19×	`pow1/3_binary64_2206` `cbrt-prod_binary64_2155`
18×	`sqrt-pow1_binary64_2142`
12×	`times-frac_binary64_2130`
11×	`pow-flip_binary64_2198`
10×	`add-exp-log_binary64_2162`
6×	`pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `swap-sqr_binary64_2091` `associate-l_binary64_2065` `associate-r_binary64_2064` `pow-sqr_binary64_2097` `add-cbrt-cube_binary64_2160`
5×	`sqrt-prod_binary64_2140`
4×	`unswap-sqr_binary64_2092` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163`
3×	`associate-/l*_binary64_2069` `pow-plus_binary64_2187` `pow2_binary64_2205`
2×	`pow1/2_binary64_2204` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `*-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `1-exp_binary64_2168` `div-inv_binary64_2121` `inv-pow_binary64_2209` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`

Counts

4 → 115

Calls

4 calls:

8.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
8.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
4.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0ms	(cbrt.f64 PI.f64)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
0.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
0.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
0.0ms	(cbrt.f64 PI.f64)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4984	1284
1	4984	1284

prune259.0ms (2.8%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	5	16	21
Picked	0	1	1
Done	0	0	0
Total	121	20	141

Error

0.3b

Counts

141 → 20

Compiler

Compiled 6129 to 3063 computations (50% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))
0.7b	(pow.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) 3)
1.0b	(pow.f64 (exp.f64 x) x)
1.0b	(sqrt.f64 PI.f64)

rewrite122.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_2124`
18×	`add-sqr-sqrt_binary64_2146`
15×	`add-cube-cbrt_binary64_2159`
14×	`pow1_binary64_2185`
9×	`flip3-+_binary64_2127` `frac-times_binary64_2134` `flip-+_binary64_2098` `frac-add_binary64_2132`
8×	`distribute-lft-out_binary64_2075`
7×	`unpow-prod-down_binary64_2203` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`pow-unpow_binary64_2201` `swap-sqr_binary64_2091`
5×	`pow-pow_binary64_2196`
4×	`add-log-exp_binary64_2163` `associate-l_binary64_2065` `cube-prod_binary64_2152` `associate-r_binary64_2064`
3×	`sqrt-prod_binary64_2140` `associate-l/_binary64_2067` `exp-prod_binary64_2176` `associate-r/_binary64_2066` `cube-div_binary64_2153`
2×	`pow-exp_binary64_2192` `sqr-pow_binary64_2096` `pow-to-exp_binary64_2193`
1×	`unpow3_binary64_2190` `pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `pow-prod-up_binary64_2194` `cube-mult_binary64_2154` `sqrt-pow1_binary64_2142` `*-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `pow1/2_binary64_2204` `distribute-rgt-in_binary64_2074` `pow2_binary64_2205` `pow-sqr_binary64_2097` `distribute-lft-in_binary64_2073` `cbrt-unprod_binary64_2157` `rem-cube-cbrt_binary64_2147`

Counts

4 → 108

Calls

4 calls:

62.0ms	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))
26.0ms	(pow.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) 3)
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)

series92.0ms (1%)

Counts

4 → 10

Calls

4 calls:

37.0ms	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))
33.0ms	(pow.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) 3)
22.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5128	3919

prune697.0ms (7.5%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	1	17	18
Picked	0	1	1
Done	0	1	1
Total	113	25	138

Error

0.2b

Counts

138 → 25

Compiler

Compiled 13094 to 7953 computations (39.3% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.0b	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
1.0b	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0b	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2146`
28×	`pow1_binary64_2185`
22×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
19×	`pow1/3_binary64_2206` `cbrt-prod_binary64_2155`
18×	`sqrt-pow1_binary64_2142`
12×	`times-frac_binary64_2130`
11×	`pow-flip_binary64_2198`
10×	`add-exp-log_binary64_2162`
6×	`pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `swap-sqr_binary64_2091` `associate-l_binary64_2065` `associate-r_binary64_2064` `pow-sqr_binary64_2097` `add-cbrt-cube_binary64_2160`
5×	`sqrt-prod_binary64_2140`
4×	`unswap-sqr_binary64_2092` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163`
3×	`associate-/l*_binary64_2069` `pow-plus_binary64_2187` `pow2_binary64_2205`
2×	`pow1/2_binary64_2204` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `*-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `1-exp_binary64_2168` `div-inv_binary64_2121` `inv-pow_binary64_2209` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`

Counts

4 → 115

Calls

4 calls:

9.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
7.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
4.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0ms	(cbrt.f64 PI.f64)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
0.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4980	1353
1	4980	1353

prune215.0ms (2.3%)

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	20	22
Picked	0	1	1
Done	0	2	2
Total	119	25	144

Error

0.2b

Counts

144 → 25

Compiler

Compiled 5557 to 2347 computations (57.8% saved)

regimes1.0s (10.9%)

Accuracy

Total 1.1b remaining (84.9%)

Threshold costs 0b (0%)

Compiler

Compiled 16055 to 10563 computations (34.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	60
1	33	60

end0.0ms (0%)

sample5.4s (58.4%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
104.0ms	8114×	pre	128	true
22.0ms	114×	body	128	invalid

Compiler

Compiled 5424 to 3571 computations (34.2% saved)

Details

analyze9.0ms (0.1%)

sample77.0ms (0.8%)

simplify175.0ms (1.9%)

prune9.0ms (0.1%)

localize18.0ms (0.2%)

rewrite96.0ms (1%)

series158.0ms (1.7%)

simplify124.0ms (1.3%)

prune369.0ms (4%)

localize30.0ms (0.3%)

rewrite39.0ms (0.4%)

series0.0ms (0%)

simplify76.0ms (0.8%)

prune259.0ms (2.8%)

localize35.0ms (0.4%)

rewrite122.0ms (1.3%)

series92.0ms (1%)

simplify94.0ms (1%)

prune697.0ms (7.5%)

localize31.0ms (0.3%)

rewrite39.0ms (0.4%)

series0.0ms (0%)

simplify67.0ms (0.7%)

prune215.0ms (2.3%)

regimes1.0s (10.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.4s (58.4%)

Profiling