Details

analyze1.1s (6.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample233.0ms (1.4%)

Algorithm

1×

intervals

Results

70.0ms	129×	body	1024	valid
66.0ms	128×	body	1024	nan
24.0ms	69×	body	512	nan
21.0ms	56×	body	512	valid
19.0ms	16×	body	2048	valid
9.0ms	34×	body	256	valid
6.0ms	24×	body	256	nan
3.0ms	21×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify271.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4731	55
1	4731	55

prune13.0ms (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: 61.1b

Counts

2 → 2

Compiler

Compiled 170 to 132 computations (22.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.8b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))
5.2b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))

rewrite64.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`distribute-lft-out_binary64` `2sinh-undef_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `2cosh-undef_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-r*_binary64`
5×	`associate-/l*_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 138

Calls

4 calls:

19.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))
8.0ms	(*.f64 (/.f64 PI.f64 4) f)
8.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))

series409.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))
89.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))
43.0ms	(*.f64 (/.f64 PI.f64 4) f)
36.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify129.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4861	5208
1	4861	5208

prune418.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	147	5	152

Merged error: 1.4b

Counts

152 → 5

Compiler

Compiled 7584 to 5786 computations (23.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.4b	(.f64 (/.f64 1 (/.f64 PI.f64 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (.f64 2 (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))))
1.0b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (.f64 2 (sinh.f64 (.f64 (/.f64 PI.f64 4) f))))

rewrite79.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`times-frac_binary64`
86×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
70×	`associate-l_binary64`
62×	`add-cube-cbrt_binary64`
38×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
20×	`log-prod_binary64`
12×	`prod-exp_binary64`
11×	`pow1_binary64` `div-exp_binary64`
10×	`associate-r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
9×	`unswap-sqr_binary64` `div-inv_binary64`
8×	`cbrt-unprod_binary64`
7×	`cbrt-undiv_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `associate-/r/_binary64` `2cosh-undef_binary64`
3×	`pow-prod-down_binary64` `sinh-def_binary64` `associate-r/_binary64` `associate-l/_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `1-exp_binary64` `rec-exp_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 185

Calls

4 calls:

23.0ms	(.f64 (/.f64 1 (/.f64 PI.f64 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (.f64 2 (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))))
10.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (.f64 2 (sinh.f64 (.f64 (/.f64 PI.f64 4) f))))
8.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

series1.1s (6.5%)

Counts

4 → 12

Calls

4 calls:

692.0ms	(.f64 (/.f64 1 (/.f64 PI.f64 4)) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (.f64 2 (sinh.f64 (*.f64 (/.f64 PI.f64 4) f))))))
342.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (.f64 2 (sinh.f64 (.f64 (/.f64 PI.f64 4) f))))
37.0ms	(*.f64 (/.f64 PI.f64 4) f)
36.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify124.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4918	5777
1	4918	5777

prune839.0ms (4.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	189	8	197
Fresh	0	3	3
Picked	0	1	1
Done	1	0	1
Total	190	12	202

Merged error: 1.0b

Counts

202 → 12

Compiler

Compiled 14562 to 11516 computations (20.9% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))
1.0b	(.f64 (/.f64 4 PI.f64) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))) 2)))
1.1b	(/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
2.6b	(log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))))) 2))

rewrite77.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
25×	`cbrt-prod_binary64`
21×	`log-prod_binary64`
17×	`add-exp-log_binary64`
13×	`associate-l_binary64`
10×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-/l*_binary64`
7×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
5×	`distribute-lft-out_binary64` `div-inv_binary64` `2cosh-undef_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `associate-r_binary64` `div-exp_binary64`
3×	`associate-/r*_binary64` `rem-log-exp_binary64` `prod-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `unswap-sqr_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sinh-def_binary64` `pow1/3_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 131

Calls

4 calls:

18.0ms	(.f64 (/.f64 4 PI.f64) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))) 2)))
12.0ms	(log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))))) 2))
9.0ms	(/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
5.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))

series2.4s (14.1%)

Counts

4 → 12

Calls

4 calls:

776.0ms	(.f64 (/.f64 4 PI.f64) (log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))) 2)))
689.0ms	(/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))) (sinh.f64 (*.f64 (/.f64 PI.f64 4) f)))
684.0ms	(log.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))) (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))))) 2))
257.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))

simplify111.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4925	7151
1	4925	7151

prune763.0ms (4.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	143	12	155

Merged error: 1.0b

Counts

155 → 12

Compiler

Compiled 10868 to 8390 computations (22.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(/.f64 (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4) f)))) (/.f64 PI.f64 4))
1.0b	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4) f)))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`times-frac_binary64`
87×	`add-sqr-sqrt_binary64`
77×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
26×	`associate-l_binary64`
22×	`pow1_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`associate-/r*_binary64`
14×	`log-pow_binary64`
9×	`div-inv_binary64`
7×	`associate-/l*_binary64`
6×	`associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-/l/_binary64` `sinh-def_binary64` `div-sub_binary64` `log-div_binary64` `cosh-def_binary64`

Counts

4 → 178

Calls

4 calls:

10.0ms	(/.f64 (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4) f)))) (/.f64 PI.f64 4))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
5.0ms	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4) f)))

series1.0s (6.1%)

Counts

4 → 12

Calls

4 calls:

647.0ms	(/.f64 (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4) f)))) (/.f64 PI.f64 4))
312.0ms	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4) f)))
42.0ms	(*.f64 (/.f64 PI.f64 4) f)
42.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5624	6329

prune580.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	4	5	9
Picked	1	0	1
Done	2	0	2
Total	195	7	202

Merged error: 1.0b

Counts

202 → 7

Compiler

Compiled 10684 to 8242 computations (22.9% saved)

regimes51.0ms (0.3%)

Compiler: Compiled 530 to 434 computations (18.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	136	40
1	136	40

end0.0ms (0%)

sample7.0s (41.2%)

Algorithm

1×

intervals

Results

2.1s	3941×	body	1024	valid
1.9s	3930×	body	1024	nan
720.0ms	1942×	body	512	valid
658.0ms	1918×	body	512	nan
523.0ms	473×	body	2048	valid
268.0ms	999×	body	256	valid
229.0ms	974×	body	256	nan
91.0ms	645×	body	128	valid
1.0ms	1×	body	2048	nan
1.0ms	4×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 320 to 262 computations (18.1% saved)

Details

analyze1.1s (6.4%)

sample233.0ms (1.4%)

simplify271.0ms (1.6%)

prune13.0ms (0.1%)

localize17.0ms (0.1%)

rewrite64.0ms (0.4%)

series409.0ms (2.4%)

simplify129.0ms (0.8%)

prune418.0ms (2.4%)

localize17.0ms (0.1%)

rewrite79.0ms (0.5%)

series1.1s (6.5%)

simplify124.0ms (0.7%)

prune839.0ms (4.9%)

localize30.0ms (0.2%)

rewrite77.0ms (0.5%)

series2.4s (14.1%)

simplify111.0ms (0.7%)

prune763.0ms (4.5%)

localize11.0ms (0.1%)

rewrite51.0ms (0.3%)

series1.0s (6.1%)

simplify99.0ms (0.6%)

prune580.0ms (3.4%)

regimes51.0ms (0.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.0s (41.2%)

Profiling