Details

analyze190.0ms (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
12.5%	43.7%	43.8%	7
12.5%	43.7%	43.8%	8
25%	28.1%	47%	9
28.1%	20.3%	51.6%	10
28.1%	20.3%	51.6%	11
34.3%	13.3%	52.4%	12
35.9%	9.8%	54.4%	13
35.9%	9.8%	54.4%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify196.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	682	18
1	682	18

prune3.0ms (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: 0.1b

Counts

2 → 1

Compiler

Compiled 24 to 22 computations (8.3% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
0.0b	(+.f64 (-.f64 1 z) (log.f64 z))
0.1b	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_8839`
9×	`pow1_binary64_8897`
8×	`add-log-exp_binary64_8875` `distribute-lft-out_binary64_8792` `add-sqr-sqrt_binary64_8860`
7×	`associate-r_binary64_8781`
6×	`add-cube-cbrt_binary64_8871`
5×	`add-cbrt-cube_binary64_8872` `add-exp-log_binary64_8874` `associate-+r+_binary64_8773`
4×	`log-pow_binary64_8925` `distribute-lft-out--_binary64_8793`
3×	`flip3-+_binary64_8842` `associate-l_binary64_8782` `sum-log_binary64_8927` `log-prod_binary64_8922` `flip-+_binary64_8813`
2×	`distribute-lft-in_binary64_8790` `distribute-rgt-in_binary64_8791` `+-commutative_binary64_8771` `associate-*r/_binary64_8783`
1×	`pow-prod-down_binary64_8907` `unswap-sqr_binary64_8807` `associate-+l+_binary64_8774` `prod-exp_binary64_8885` `sub-neg_binary64_8832` `cbrt-unprod_binary64_8869` `*-commutative_binary64_8772` `associate-+l-_binary64_8776` `diff-log_binary64_8928`

Counts

3 → 60

Calls

3 calls:

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

series324.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

115.0ms	(+.f64 (-.f64 1 z) (log.f64 z))
114.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
95.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

simplify86.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4939	1039
1	4939	1039

prune79.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	6	70

Merged error: 0.0b

Counts

70 → 6

Compiler

Compiled 1302 to 817 computations (37.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))
0.1b	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z))))
0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_8839`
12×	`add-sqr-sqrt_binary64_8860`
10×	`add-log-exp_binary64_8875` `add-cube-cbrt_binary64_8871`
9×	`cbrt-prod_binary64_8867`
8×	`pow1_binary64_8897`
6×	`add-cbrt-cube_binary64_8872` `add-exp-log_binary64_8874` `associate-+r+_binary64_8773` `log-prod_binary64_8922`
5×	`sum-log_binary64_8927` `associate-r_binary64_8781`
4×	`distribute-lft-out_binary64_8792`
3×	`associate-l_binary64_8782`
2×	`flip3-+_binary64_8842` `log-pow_binary64_8925` `flip-+_binary64_8813` `pow1/3_binary64_8918` `associate-+l-_binary64_8776` `associate-*r/_binary64_8783`
1×	`pow-prod-down_binary64_8907` `unswap-sqr_binary64_8807` `associate-+l+_binary64_8774` `prod-exp_binary64_8885` `distribute-lft-in_binary64_8790` `cbrt-unprod_binary64_8869` `distribute-rgt-in_binary64_8791` `*-commutative_binary64_8772` `+-commutative_binary64_8771` `diff-log_binary64_8928`

Counts

4 → 69

Calls

4 calls:

14.0ms	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z))))
13.0ms	(+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)

series890.0ms (18.1%)

Counts

4 → 12

Calls

4 calls:

338.0ms	(+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))
252.0ms	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z))))
158.0ms	(cbrt.f64 z)
142.0ms	(cbrt.f64 z)

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4910	996
1	4910	996

prune98.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	80	7	87

Merged error: 0b

Counts

87 → 7

Compiler

Compiled 1837 to 1023 computations (44.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (log.f64 z) z)
0.0b	(+.f64 (.f64 x 1/2) (+.f64 y (.f64 (-.f64 (log.f64 z) z) y)))
0.2b	(*.f64 (-.f64 (log.f64 z) z) y)
0.2b	(+.f64 y (*.f64 (-.f64 (log.f64 z) z) y))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_8839`
13×	`add-sqr-sqrt_binary64_8860`
12×	`add-log-exp_binary64_8875`
8×	`pow1_binary64_8897`
7×	`add-cube-cbrt_binary64_8871`
6×	`add-cbrt-cube_binary64_8872` `add-exp-log_binary64_8874` `associate-l_binary64_8782`
4×	`sum-log_binary64_8927` `distribute-lft-out--_binary64_8793`
3×	`associate--l+_binary64_8778` `log-prod_binary64_8922` `associate-r_binary64_8781`
2×	`flip3--_binary64_8843` `flip3-+_binary64_8842` `flip--_binary64_8814` `associate-*l/_binary64_8784` `log-pow_binary64_8925` `flip-+_binary64_8813` `+-commutative_binary64_8771` `difference-of-squares_binary64_8808`
1×	`distribute-rgt1-in_binary64_8797` `pow-prod-down_binary64_8907` `unswap-sqr_binary64_8807` `prod-exp_binary64_8885` `associate-+r+_binary64_8773` `sub-neg_binary64_8832` `cbrt-unprod_binary64_8869` `*-commutative_binary64_8772` `distribute-rgt-out_binary64_8794` `diff-log_binary64_8928`

Counts

4 → 66

Calls

4 calls:

8.0ms	(*.f64 (-.f64 (log.f64 z) z) y)
7.0ms	(-.f64 (log.f64 z) z)
7.0ms	(+.f64 (.f64 x 1/2) (+.f64 y (.f64 (-.f64 (log.f64 z) z) y)))
4.0ms	(+.f64 y (*.f64 (-.f64 (log.f64 z) z) y))

series403.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(+.f64 y (*.f64 (-.f64 (log.f64 z) z) y))
110.0ms	(-.f64 (log.f64 z) z)
98.0ms	(+.f64 (.f64 x 1/2) (+.f64 y (.f64 (-.f64 (log.f64 z) z) y)))
83.0ms	(*.f64 (-.f64 (log.f64 z) z) y)

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4954	1133
1	4954	1133

prune75.0ms (1.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	78	7	85

Merged error: 0b

Counts

85 → 7

Compiler

Compiled 1457 to 590 computations (59.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) (cbrt.f64 (-.f64 (log.f64 z) z)))
0.5b	(cbrt.f64 (-.f64 (log.f64 z) z))
0.5b	(cbrt.f64 (-.f64 (log.f64 z) z))
0.5b	(cbrt.f64 (-.f64 (log.f64 z) z))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`cbrt-prod_binary64_8867`
52×	`*-un-lft-identity_binary64_8839`
37×	`add-sqr-sqrt_binary64_8860`
22×	`pow1_binary64_8897` `distribute-lft-out--_binary64_8793`
18×	`cbrt-div_binary64_8868`
15×	`swap-sqr_binary64_8806` `add-cube-cbrt_binary64_8871`
11×	`log-pow_binary64_8925`
9×	`flip3--_binary64_8843` `associate-l_binary64_8782` `flip--_binary64_8814` `pow1/3_binary64_8918` `associate-r_binary64_8781`
7×	`difference-of-squares_binary64_8808`
6×	`add-exp-log_binary64_8874`
4×	`add-log-exp_binary64_8875` `add-cbrt-cube_binary64_8872` `unswap-sqr_binary64_8807` `frac-times_binary64_8849`
2×	`pow-prod-down_binary64_8907` `pow-sqr_binary64_8812` `pow-prod-up_binary64_8906` `associate-l/_binary64_8784` `associate-r/_binary64_8783`
1×	`pow-plus_binary64_8899` `pow2_binary64_8917` `prod-exp_binary64_8885` `cbrt-unprod_binary64_8869` `*-commutative_binary64_8772`

Counts

4 → 111

Calls

4 calls:

14.0ms	(*.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) (cbrt.f64 (-.f64 (log.f64 z) z)))
4.0ms	(cbrt.f64 (-.f64 (log.f64 z) z))
4.0ms	(cbrt.f64 (-.f64 (log.f64 z) z))
4.0ms	(cbrt.f64 (-.f64 (log.f64 z) z))

series363.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(*.f64 (cbrt.f64 (-.f64 (log.f64 z) z)) (cbrt.f64 (-.f64 (log.f64 z) z)))
94.0ms	(cbrt.f64 (-.f64 (log.f64 z) z))
86.0ms	(cbrt.f64 (-.f64 (log.f64 z) z))
80.0ms	(cbrt.f64 (-.f64 (log.f64 z) z))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4950	2793
1	4950	2793

prune156.0ms (3.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	123	7	130

Merged error: 0b

Counts

130 → 7

Compiler

Compiled 4160 to 1447 computations (65.2% saved)

regimes470.0ms (9.6%)

Compiler: Compiled 3473 to 2656 computations (23.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	18
1	26	18

end0.0ms (0%)

sample1.1s (23.3%)

Algorithm

1×

intervals

Results

406.0ms	8000×	body	128	valid
16.0ms	294×	body	128	invalid
2.0ms	63×	body	128	nan

Compiler

Compiled 524 to 404 computations (22.9% saved)

Details

analyze190.0ms (3.9%)

sample22.0ms (0.4%)

simplify196.0ms (4%)

prune3.0ms (0.1%)

localize13.0ms (0.3%)

rewrite32.0ms (0.7%)

series324.0ms (6.6%)

simplify86.0ms (1.8%)

prune79.0ms (1.6%)

localize14.0ms (0.3%)

rewrite36.0ms (0.7%)

series890.0ms (18.1%)

simplify78.0ms (1.6%)

prune98.0ms (2%)

localize10.0ms (0.2%)

rewrite31.0ms (0.6%)

series403.0ms (8.2%)

simplify69.0ms (1.4%)

prune75.0ms (1.5%)

localize14.0ms (0.3%)

rewrite40.0ms (0.8%)

series363.0ms (7.4%)

simplify70.0ms (1.4%)

prune156.0ms (3.2%)

regimes470.0ms (9.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (23.3%)

Profiling