Details

analyze1.1s (15.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
13.1%	74.3%	12.7%	12
16.1%	70.5%	13.5%	13
18.6%	68%	13.5%	14

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample101.0ms (1.4%)

Algorithm

1×

intervals

Results

28.0ms	47×	body	1280	valid
20.0ms	60×	body	640	valid
10.0ms	7×	body	2560	valid
9.0ms	23×	body	320	valid
7.0ms	105×	body	80	valid
4.0ms	17×	body	640	nan
3.0ms	9×	body	1280	nan
2.0ms	14×	body	160	valid
2.0ms	36×	body	80	nan
1.0ms	26×	body	80	overflowed
1.0ms	8×	body	320	nan

Compiler

Compiled 27 to 29 computations (-7.4% saved)

simplify327.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (318.0ms)

Iter	Nodes	Cost
0	4990	20
1	4990	20

prune5.0ms (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: 27.3b

Counts

2 → 1

Compiler

Compiled 26 to 24 computations (7.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (exp.f64 z))
0.1b	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
2.4b	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
3.4b	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
9×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`associate-/l*_binary64` `log-div_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-r_binary64` `log-prod_binary64` `associate-l*_binary64` `flip-+_binary64`
2×	`div-sub_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

9.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
8.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
7.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
5.0ms	(*.f64 y (exp.f64 z))

series65.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
15.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
7.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
5.0ms	(*.f64 y (exp.f64 z))

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5031	1971

prune306.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	8	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 5.3b

Counts

92 → 8

Compiler

Compiled 2117 to 1144 computations (46% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.0b	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
3.5b	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
6.3b	(.f64 y (.f64 z z))
7.8b	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
23×	`pow1_binary64`
18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`times-frac_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
4×	`sub-neg_binary64` `associate-l_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `flip-+_binary64` `associate-+r+_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 92

Calls

4 calls:

13.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
9.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)
6.0ms	(.f64 y (.f64 z z))
6.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))

series67.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)
15.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
13.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
7.0ms	(.f64 y (.f64 z z))

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5367	2252

prune116.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	100	12	112

Merged error: 5.2b

Counts

112 → 12

Compiler

Compiled 2967 to 1558 computations (47.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.0b	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
3.5b	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
6.3b	(.f64 y (.f64 z z))
7.8b	(.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))) (/.f64 1 t))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
25×	`pow1_binary64` `add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
18×	`*-un-lft-identity_binary64`
17×	`prod-exp_binary64`
15×	`cbrt-unprod_binary64`
14×	`pow-prod-down_binary64` `add-cube-cbrt_binary64`
11×	`times-frac_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64`
4×	`sub-neg_binary64` `unswap-sqr_binary64`
3×	`flip3-+_binary64` `associate-r/_binary64` `flip-+_binary64` `-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `div-exp_binary64` `associate-+r+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`flip3--_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 103

Calls

4 calls:

16.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
11.0ms	(.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))) (/.f64 1 t))
6.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
6.0ms	(.f64 y (.f64 z z))

series63.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))) (/.f64 1 t))
15.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
13.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
7.0ms	(.f64 y (.f64 z z))

simplify113.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5055	2638

prune123.0ms (1.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	113	14	127

Merged error: 5.2b

Counts

127 → 14

Compiler

Compiled 3527 to 1820 computations (48.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1 (/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))))
2.6b	(.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))
3.7b	(.f64 (-.f64 1 y) (.f64 1/2 (*.f64 z z)))
7.8b	(/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z))))))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64`
41×	`add-exp-log_binary64`
32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
29×	`add-cbrt-cube_binary64`
27×	`add-cube-cbrt_binary64`
16×	`pow1_binary64`
14×	`div-exp_binary64`
12×	`associate-*r/_binary64`
11×	`associate-/r/_binary64` `prod-exp_binary64`
10×	`associate-/r*_binary64`
9×	`cbrt-unprod_binary64` `associate-l_binary64`
7×	`pow-prod-down_binary64` `cbrt-undiv_binary64`
6×	`flip3-+_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64`
3×	`1-exp_binary64` `rec-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `pow-flip_binary64`

Counts

4 → 135

Calls

4 calls:

12.0ms	(.f64 (-.f64 1 y) (.f64 1/2 (*.f64 z z)))
9.0ms	(/.f64 1 (/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))))
7.0ms	(/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z))))))
6.0ms	(.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))

series113.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z))))))
38.0ms	(/.f64 1 (/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))))
16.0ms	(.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))
14.0ms	(.f64 (-.f64 1 y) (.f64 1/2 (*.f64 z z)))

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5107	3806

prune139.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	142	5	147
Fresh	4	8	12
Picked	1	0	1
Done	1	0	1
Total	148	13	161

Merged error: 3.3b

Counts

161 → 13

Compiler

Compiled 3907 to 2291 computations (41.4% saved)

regimes375.0ms (5.1%)

Compiler: Compiled 1815 to 1437 computations (20.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 5 computations (-150% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	291	65
1	291	65

end0.0ms (0%)

sample3.8s (52.3%)

Algorithm

1×

intervals

Results

877.0ms	1493×	body	1280	valid
513.0ms	1523×	body	640	valid
251.0ms	3535×	body	80	valid
191.0ms	886×	body	320	valid
160.0ms	116×	body	2560	valid
72.0ms	296×	body	640	nan
68.0ms	1497×	body	80	nan
59.0ms	447×	body	160	valid
45.0ms	822×	body	80	overflowed
40.0ms	113×	body	1280	nan
30.0ms	187×	body	320	nan
12.0ms	120×	body	160	nan
1.0ms	17×	body	80	invalid
1.0ms	4×	body	320	invalid
0.0ms	1×	body	640	invalid

Compiler

Compiled 427 to 328 computations (23.2% saved)

Details

analyze1.1s (15.3%)

sample101.0ms (1.4%)

simplify327.0ms (4.5%)

prune5.0ms (0.1%)

localize9.0ms (0.1%)

rewrite32.0ms (0.4%)

series65.0ms (0.9%)

simplify75.0ms (1%)

prune306.0ms (4.2%)

localize12.0ms (0.2%)

rewrite38.0ms (0.5%)

series67.0ms (0.9%)

simplify88.0ms (1.2%)

prune116.0ms (1.6%)

localize13.0ms (0.2%)

rewrite42.0ms (0.6%)

series63.0ms (0.9%)

simplify113.0ms (1.6%)

prune123.0ms (1.7%)

localize14.0ms (0.2%)

rewrite39.0ms (0.5%)

series113.0ms (1.6%)

simplify72.0ms (1%)

prune139.0ms (1.9%)

regimes375.0ms (5.1%)

bsearch1.0ms (0%)

simplify11.0ms (0.2%)

end0.0ms (0%)

sample3.8s (52.3%)

Profiling