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)

sample36.0ms (0.6%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify218.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (200.0ms)

Iter	Nodes	Cost
0	5204	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)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

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 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 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite96.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`add-exp-log_binary64`
76×	`prod-exp_binary64`
75×	`add-cbrt-cube_binary64`
48×	`associate-l_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`cbrt-unprod_binary64`
40×	`times-frac_binary64`
36×	`pow1_binary64`
35×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
22×	`pow-prod-down_binary64`
15×	`div-exp_binary64` `associate-*l/_binary64`
14×	`sqrt-prod_binary64`
12×	`frac-add_binary64`
9×	`cbrt-undiv_binary64`
6×	`flip3-+_binary64` `1-exp_binary64` `associate-*r/_binary64` `rec-exp_binary64` `flip-+_binary64` `frac-times_binary64`
5×	`associate-r_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`div-inv_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 173

Calls

4 calls:

36.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
33.0ms	(.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)))))
15.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
2.0ms	(sqrt.f64 PI.f64)

series720.0ms (11%)

Counts

4 → 10

Calls

4 calls:

523.0ms	(.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)))))
108.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
89.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify214.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4898	5483
1	4898	5483

prune587.0ms (9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	180	5	185

Merged error: 0b

Counts

185 → 5

Compiler

Compiled 11352 to 5260 computations (53.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
30×	`sqrt-prod_binary64`
12×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `flip-+_binary64`

Counts

4 → 110

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
5.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series332.0ms (5.1%)

Counts

4 → 6

Calls

4 calls:

332.0ms	(/.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)

simplify175.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4927	3230
1	4927	3230

prune262.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	116	5	121

Merged error: 0b

Counts

121 → 5

Compiler

Compiled 4874 to 3064 computations (37.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.3b	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`associate-r_binary64`
18×	`times-frac_binary64`
16×	`add-exp-log_binary64`
15×	`sqrt-prod_binary64`
10×	`add-cbrt-cube_binary64`
8×	`unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`associate-/r_binary64` `associate-l*_binary64` `prod-exp_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `cube-prod_binary64` `insert-posit16`
3×	`associate-/l*_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 114

Calls

4 calls:

18.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
7.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
2.0ms	(sqrt.f64 PI.f64)

series687.0ms (10.6%)

Counts

4 → 10

Calls

4 calls:

513.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
101.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
74.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.0ms	(sqrt.f64 PI.f64)

simplify115.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5580	3925

prune278.0ms (4.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	124	5	129

Merged error: 0b

Counts

129 → 5

Compiler

Compiled 4950 to 3271 computations (33.9% saved)

localize28.0ms (0.4%)

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)) (log.f64 (exp.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (.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 2/3 (pow.f64 (fabs.f64 x) 3))
1.0b	(sqrt.f64 PI.f64)
1.9b	(log.f64 (exp.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
25×	`associate-l_binary64`
24×	`add-cube-cbrt_binary64`
22×	`times-frac_binary64`
18×	`add-exp-log_binary64`
15×	`associate-r_binary64`
14×	`sqrt-prod_binary64`
13×	`associate-*l/_binary64`
12×	`frac-add_binary64`
11×	`add-cbrt-cube_binary64`
9×	`unswap-sqr_binary64`
8×	`pow1_binary64`
7×	`prod-exp_binary64`
6×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64` `frac-times_binary64`
5×	`add-log-exp_binary64`
4×	`unpow-prod-down_binary64` `cube-prod_binary64` `insert-posit16`
3×	`cbrt-unprod_binary64` `log-prod_binary64` `log-pow_binary64`
2×	`sqr-pow_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `div-inv_binary64` `exp-to-pow_binary64` `pow-exp_binary64` `unpow3_binary64` `exp-prod_binary64` `cube-mult_binary64`

Counts

4 → 122

Calls

4 calls:

34.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (log.f64 (exp.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (.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)))))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
2.0ms	(log.f64 (exp.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))
2.0ms	(sqrt.f64 PI.f64)

series675.0ms (10.4%)

Counts

4 → 10

Calls

4 calls:

526.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (log.f64 (exp.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3))))) (.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)))))
74.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
74.0ms	(log.f64 (exp.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))))
0.0ms	(sqrt.f64 PI.f64)

simplify163.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4953	4847
1	4953	4847

prune378.0ms (5.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	132	5	137

Merged error: 0b

Counts

137 → 5

Compiler

Compiled 8106 to 3940 computations (51.4% saved)

regimes132.0ms (2%)

Compiler: Compiled 1509 to 863 computations (42.8% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	101
1	44	101

end0.0ms (0%)

sample1.2s (18.7%)

Algorithm

1×

intervals

Results

764.0ms	8000×	body	80	valid
101.0ms	8002×	pre	80	true
0.0ms	2×	body	80	invalid

Compiler

Compiled 354 to 196 computations (44.6% saved)

Details

analyze6.0ms (0.1%)

sample36.0ms (0.6%)

simplify218.0ms (3.4%)

prune7.0ms (0.1%)

localize26.0ms (0.4%)

rewrite96.0ms (1.5%)

series720.0ms (11%)

simplify214.0ms (3.3%)

prune587.0ms (9%)

localize20.0ms (0.3%)

rewrite27.0ms (0.4%)

series332.0ms (5.1%)

simplify175.0ms (2.7%)

prune262.0ms (4%)

localize19.0ms (0.3%)

rewrite38.0ms (0.6%)

series687.0ms (10.6%)

simplify115.0ms (1.8%)

prune278.0ms (4.3%)

localize28.0ms (0.4%)

rewrite54.0ms (0.8%)

series675.0ms (10.4%)

simplify163.0ms (2.5%)

prune378.0ms (5.8%)

regimes132.0ms (2%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.2s (18.7%)

Profiling