Details

analyze6.0ms (0.1%)

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)

sample38.0ms (0.8%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify269.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	5203	47

prune7.0ms (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

Merged error: 0.0b

Counts

2 → 2

Compiler

Compiled 125 to 77 computations (38.4% saved)

localize28.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

rewrite126.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`add-exp-log_binary64_2134`
76×	`prod-exp_binary64_2145`
75×	`add-cbrt-cube_binary64_2132`
48×	`associate-l_binary64_2042`
46×	`add-sqr-sqrt_binary64_2120`
44×	`cbrt-unprod_binary64_2129`
40×	`times-frac_binary64_2105`
36×	`pow1_binary64_2157`
35×	`*-un-lft-identity_binary64_2099`
33×	`add-cube-cbrt_binary64_2131`
22×	`pow-prod-down_binary64_2167`
15×	`div-exp_binary64_2147` `associate-*l/_binary64_2044`
14×	`sqrt-prod_binary64_2114`
12×	`frac-add_binary64_2107`
9×	`cbrt-undiv_binary64_2130`
6×	`associate-*r/_binary64_2043` `flip3-+_binary64_2102` `1-exp_binary64_2140` `rec-exp_binary64_2146` `frac-times_binary64_2109` `flip-+_binary64_2073`
5×	`unswap-sqr_binary64_2067` `associate-r_binary64_2041`
4×	`add-log-exp_binary64_2135`
3×	`*-commutative_binary64_2032` `div-inv_binary64_2096`
1×	`distribute-rgt-in_binary64_2051` `distribute-lft-in_binary64_2050` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `sqrt-pow1_binary64_2116`

Counts

4 → 169

Calls

4 calls:

35.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
31.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
13.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
2.0ms	(sqrt.f64 PI.f64)

series734.0ms (14.8%)

Counts

4 → 10

Calls

4 calls:

557.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
104.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
73.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify122.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5010	5420

prune508.0ms (10.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	175	6	181

Merged error: 0.0b

Counts

181 → 6

Compiler

Compiled 11208 to 5239 computations (53.3% saved)

localize28.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_2120` `cbrt-prod_binary64_2127`
19×	`pow1_binary64_2157`
14×	`add-cube-cbrt_binary64_2131` `pow1/3_binary64_2178` `*-un-lft-identity_binary64_2099`
9×	`sqrt-pow1_binary64_2116`
6×	`associate-l_binary64_2042` `associate-r_binary64_2041` `add-exp-log_binary64_2134` `swap-sqr_binary64_2066`
4×	`add-cbrt-cube_binary64_2132` `add-log-exp_binary64_2135` `pow-prod-down_binary64_2167` `unswap-sqr_binary64_2067` `pow-prod-up_binary64_2166` `pow-sqr_binary64_2072`
2×	`pow2_binary64_2177` `pow-plus_binary64_2159`
1×	`*-commutative_binary64_2032` `prod-exp_binary64_2145` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `cbrt-unprod_binary64_2129` `sqrt-prod_binary64_2114`

Counts

4 → 81

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
5.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

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

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4980	845
1	4980	845

prune180.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	85	6	91

Merged error: 0b

Counts

91 → 6

Compiler

Compiled 3639 to 2233 computations (38.6% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_2120`
36×	`add-cube-cbrt_binary64_2131` `times-frac_binary64_2105` `*-un-lft-identity_binary64_2099`
30×	`sqrt-prod_binary64_2114`
12×	`associate-/r*_binary64_2045`
8×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
6×	`pow1_binary64_2157` `associate-/l*_binary64_2046`
4×	`add-log-exp_binary64_2135`
2×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `associate-/l/_binary64_2048` `frac-2neg_binary64_2110` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `clear-num_binary64_2098` `div-inv_binary64_2096` `sqrt-pow1_binary64_2116`
1×	`flip3-+_binary64_2102` `flip-+_binary64_2073`

Counts

4 → 106

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (sqrt.f64 PI.f64))
4.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series372.0ms (7.5%)

Counts

4 → 6

Calls

4 calls:

372.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (sqrt.f64 PI.f64))
0.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5009	3173

prune240.0ms (4.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	113	5	118

Merged error: 0b

Counts

118 → 5

Compiler

Compiled 4682 to 2948 computations (37% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64_2120`
40×	`times-frac_binary64_2105`
37×	`*-un-lft-identity_binary64_2099`
35×	`add-cube-cbrt_binary64_2131`
29×	`sqrt-prod_binary64_2114`
22×	`associate-r_binary64_2041`
15×	`add-exp-log_binary64_2134`
11×	`add-cbrt-cube_binary64_2132`
8×	`pow1_binary64_2157`
6×	`associate-/r*_binary64_2045`
5×	`unswap-sqr_binary64_2067`
4×	`prod-exp_binary64_2145` `add-log-exp_binary64_2135`
3×	`associate-l_binary64_2042` `div-exp_binary64_2147` `associate-/l*_binary64_2046`
2×	`cbrt-undiv_binary64_2130` `associate-/l/_binary64_2048` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `div-inv_binary64_2096` `sqrt-pow1_binary64_2116` `cbrt-unprod_binary64_2129`
1×	`associate-r/_binary64_2043` `flip3-+_binary64_2102` `1-exp_binary64_2140` `un-div-inv_binary64_2097` `-commutative_binary64_2032` `rec-exp_binary64_2146` `frac-2neg_binary64_2110` `pow-prod-down_binary64_2167` `clear-num_binary64_2098` `flip-+_binary64_2073`

Counts

4 → 114

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (sqrt.f64 PI.f64))
12.0ms	(*.f64 1/21 (/.f64 1 (sqrt.f64 PI.f64)))
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series342.0ms (6.9%)

Counts

4 → 6

Calls

4 calls:

342.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (sqrt.f64 PI.f64))
0.0ms	(*.f64 1/21 (/.f64 1 (sqrt.f64 PI.f64)))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify102.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4914	2998
1	4914	2998

prune271.0ms (5.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	120	5	125

Merged error: 0b

Counts

125 → 5

Compiler

Compiled 5087 to 3270 computations (35.7% saved)

regimes126.0ms (2.5%)

Compiler: Compiled 1424 to 858 computations (39.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	101
1	43	101

end0.0ms (0%)

sample1.2s (23.8%)

Algorithm

1×

intervals

Results

746.0ms	8000×	body	128	valid
96.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 337 to 195 computations (42.1% saved)

Details

analyze6.0ms (0.1%)

sample38.0ms (0.8%)

simplify269.0ms (5.4%)

prune7.0ms (0.1%)

localize28.0ms (0.6%)

rewrite126.0ms (2.5%)

series734.0ms (14.8%)

simplify122.0ms (2.5%)

prune508.0ms (10.2%)

localize28.0ms (0.6%)

rewrite24.0ms (0.5%)

series0.0ms (0%)

simplify68.0ms (1.4%)

prune180.0ms (3.6%)

localize19.0ms (0.4%)

rewrite35.0ms (0.7%)

series372.0ms (7.5%)

simplify62.0ms (1.3%)

prune240.0ms (4.8%)

localize23.0ms (0.5%)

rewrite45.0ms (0.9%)

series342.0ms (6.9%)

simplify102.0ms (2.1%)

prune271.0ms (5.5%)

regimes126.0ms (2.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (23.8%)

Profiling