Details

analyze851.0ms (14.5%)

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
3.1%	71.7%	25.1%	9
4.7%	69.8%	25.5%	10
7%	66.9%	26.1%	11
10.9%	61.5%	27.6%	12
11.1%	47%	41.9%	13
12.8%	44.4%	42.8%	14

Compiler

Compiled 20 to 20 computations (0% saved)

sample60.0ms (1%)

Algorithm

1×

intervals

Results

24.0ms	297×	body	128	nan
18.0ms	256×	body	128	valid

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify194.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5398	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

Error

1.0b

Counts

2 → 2

Compiler

Compiled 45 to 45 computations (0% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (/.f64 x (.f64 y 27)))
1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
3.3b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
6.2b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-exp-log_binary64_20917`
92×	`add-cbrt-cube_binary64_20915`
41×	`prod-exp_binary64_20928`
39×	`cbrt-unprod_binary64_20912`
31×	`add-sqr-sqrt_binary64_20901`
28×	`div-exp_binary64_20930`
27×	`cbrt-undiv_binary64_20913`
21×	`associate-l_binary64_20820`
19×	`*-un-lft-identity_binary64_20879`
18×	`add-cube-cbrt_binary64_20914`
16×	`times-frac_binary64_20885` `associate-r_binary64_20819`
10×	`pow1_binary64_20940`
6×	`unswap-sqr_binary64_20847`
4×	`sqrt-prod_binary64_20895` `div-inv_binary64_20876` `add-log-exp_binary64_20918`
3×	`pow-prod-down_binary64_20950` `*-commutative_binary64_20810`
2×	`associate-r/_binary64_20821` `associate-l/_binary64_20822`
1×	`associate-/l_binary64_20824` `associate-/r_binary64_20823` `associate-/l/_binary64_20826` `rec-exp_binary64_20929` `frac-2neg_binary64_20890` `1-exp_binary64_20923` `clear-num_binary64_20878`

Counts

4 → 133

Calls

4 calls:

13.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
9.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
8.0ms	(.f64 3 (/.f64 x (.f64 y 27)))
7.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

series164.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
32.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
24.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
13.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4931	2711
1	4931	2711

prune178.0ms (3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	145	2	147

Error

0.0b

Counts

147 → 2

Compiler

Compiled 3184 to 2292 computations (28% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (*.f64 y 27))
0.2b	(.f64 3/2 (/.f64 (/.f64 x (.f64 y 27)) z))
3.3b	(.f64 (.f64 3/2 (/.f64 (/.f64 x (*.f64 y 27)) z)) (sqrt.f64 t))
6.2b	(/.f64 (/.f64 x (*.f64 y 27)) z)

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`times-frac_binary64_20885`
52×	`add-cbrt-cube_binary64_20915` `add-exp-log_binary64_20917`
44×	`add-sqr-sqrt_binary64_20901`
39×	`add-cube-cbrt_binary64_20914` `*-un-lft-identity_binary64_20879`
31×	`associate-r_binary64_20819`
17×	`div-exp_binary64_20930` `cbrt-undiv_binary64_20913` `prod-exp_binary64_20928` `cbrt-unprod_binary64_20912`
11×	`pow1_binary64_20940`
10×	`associate-/l*_binary64_20824` `div-inv_binary64_20876`
4×	`associate-l_binary64_20820` `associate-/r*_binary64_20823` `pow-prod-down_binary64_20950` `add-log-exp_binary64_20918`
3×	`sqrt-prod_binary64_20895`
2×	`frac-2neg_binary64_20890` `unswap-sqr_binary64_20847` `-commutative_binary64_20810` `clear-num_binary64_20878` `associate-r/_binary64_20821`
1×	`associate-/l/_binary64_20826` `associate-*l/_binary64_20822`

Counts

4 → 145

Calls

4 calls:

13.0ms	(.f64 (.f64 3/2 (/.f64 (/.f64 x (*.f64 y 27)) z)) (sqrt.f64 t))
13.0ms	(.f64 3/2 (/.f64 (/.f64 x (.f64 y 27)) z))
7.0ms	(/.f64 (/.f64 x (*.f64 y 27)) z)
4.0ms	(/.f64 x (*.f64 y 27))

series147.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(.f64 (.f64 3/2 (/.f64 (/.f64 x (*.f64 y 27)) z)) (sqrt.f64 t))
23.0ms	(.f64 3/2 (/.f64 (/.f64 x (.f64 y 27)) z))
23.0ms	(/.f64 (/.f64 x (*.f64 y 27)) z)
12.0ms	(/.f64 x (*.f64 y 27))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4942	2305
1	4942	2305

prune291.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	156	3	159

Error

Counts

159 → 3

Compiler

Compiled 4684 to 3480 computations (25.7% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (acos.f64 (.f64 (.f64 (/.f64 x (*.f64 y z)) 1/18) (sqrt.f64 t))) (cbrt.f64 3))
0.2b	(.f64 (/.f64 x (.f64 y z)) 1/18)
3.3b	(.f64 (.f64 (/.f64 x (*.f64 y z)) 1/18) (sqrt.f64 t))
4.8b	(/.f64 x (*.f64 y z))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_20917`
33×	`add-cbrt-cube_binary64_20915`
28×	`add-sqr-sqrt_binary64_20901`
26×	`add-cube-cbrt_binary64_20914` `*-un-lft-identity_binary64_20879`
24×	`times-frac_binary64_20885`
13×	`prod-exp_binary64_20928` `cbrt-unprod_binary64_20912`
12×	`cbrt-prod_binary64_20910`
11×	`pow1_binary64_20940`
9×	`associate-r_binary64_20819`
8×	`associate-l_binary64_20820`
7×	`associate-/r*_binary64_20823` `div-exp_binary64_20930` `cbrt-undiv_binary64_20913`
6×	`associate-/l*_binary64_20824`
4×	`pow-prod-down_binary64_20950` `add-log-exp_binary64_20918`
3×	`sqrt-prod_binary64_20895` `div-inv_binary64_20876` `associate-*l/_binary64_20822`
2×	`frac-2neg_binary64_20890` `*-commutative_binary64_20810` `clear-num_binary64_20878`
1×	`unswap-sqr_binary64_20847` `acos-asin_binary64_21060` `div-sub_binary64_20884`

Counts

4 → 114

Calls

4 calls:

10.0ms	(.f64 (.f64 (/.f64 x (*.f64 y z)) 1/18) (sqrt.f64 t))
7.0ms	(.f64 (/.f64 x (.f64 y z)) 1/18)
5.0ms	(/.f64 x (*.f64 y z))
4.0ms	(/.f64 (acos.f64 (.f64 (.f64 (/.f64 x (*.f64 y z)) 1/18) (sqrt.f64 t))) (cbrt.f64 3))

series188.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(.f64 (.f64 (/.f64 x (*.f64 y z)) 1/18) (sqrt.f64 t))
54.0ms	(/.f64 (acos.f64 (.f64 (.f64 (/.f64 x (*.f64 y z)) 1/18) (sqrt.f64 t))) (cbrt.f64 3))
22.0ms	(.f64 (/.f64 x (.f64 y z)) 1/18)
20.0ms	(/.f64 x (*.f64 y z))

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4986	2620
1	4986	2620

prune192.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	126	3	129

Error

Counts

129 → 3

Compiler

Compiled 3723 to 2564 computations (31.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/18 (/.f64 x (.f64 y z)))
1.0b	(.f64 1/3 (acos.f64 (.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (.f64 y z))))))
3.3b	(.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))
4.8b	(/.f64 x (*.f64 y z))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64_20915` `add-exp-log_binary64_20917`
17×	`add-sqr-sqrt_binary64_20901`
14×	`prod-exp_binary64_20928` `cbrt-unprod_binary64_20912`
13×	`add-cube-cbrt_binary64_20914` `*-un-lft-identity_binary64_20879` `pow1_binary64_20940`
12×	`associate-l_binary64_20820`
11×	`associate-r_binary64_20819`
6×	`times-frac_binary64_20885` `div-exp_binary64_20930` `cbrt-undiv_binary64_20913`
5×	`pow-prod-down_binary64_20950`
4×	`add-log-exp_binary64_20918`
3×	`associate-/l_binary64_20824` `sqrt-prod_binary64_20895` `-commutative_binary64_20810` `associate-*r/_binary64_20821`
2×	`unswap-sqr_binary64_20847` `div-inv_binary64_20876`
1×	`associate-/r*_binary64_20823` `frac-2neg_binary64_20890` `clear-num_binary64_20878`

Counts

4 → 92

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))
7.0ms	(.f64 1/18 (/.f64 x (.f64 y z)))
4.0ms	(/.f64 x (*.f64 y z))
4.0ms	(.f64 1/3 (acos.f64 (.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (.f64 y z))))))

series154.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))
31.0ms	(.f64 1/3 (acos.f64 (.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (.f64 y z))))))
25.0ms	(.f64 1/18 (/.f64 x (.f64 y z)))
19.0ms	(/.f64 x (*.f64 y z))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5003	1589

prune87.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	104	3	107

Error

Counts

107 → 3

Compiler

Compiled 1830 to 934 computations (49% saved)

regimes538.0ms (9.1%)

Accuracy

Total 0.2b remaining (100%)

Threshold costs 0.2b (100%)

Compiler

Compiled 5642 to 5629 computations (0.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	24	35

end0.0ms (0%)

sample2.3s (38.4%)

Algorithm

1×

intervals

Results

687.0ms	10160×	body	128	nan
580.0ms	8000×	body	128	valid

Compiler

Compiled 451 to 450 computations (0.2% saved)

Details

analyze851.0ms (14.5%)

sample60.0ms (1%)

simplify194.0ms (3.3%)

prune5.0ms (0.1%)

localize18.0ms (0.3%)

rewrite51.0ms (0.9%)

series164.0ms (2.8%)

simplify102.0ms (1.7%)

prune178.0ms (3%)

localize16.0ms (0.3%)

rewrite53.0ms (0.9%)

series147.0ms (2.5%)

simplify84.0ms (1.4%)

prune291.0ms (4.9%)

localize18.0ms (0.3%)

rewrite37.0ms (0.6%)

series188.0ms (3.2%)

simplify78.0ms (1.3%)

prune192.0ms (3.3%)

localize10.0ms (0.2%)

rewrite35.0ms (0.6%)

series154.0ms (2.6%)

simplify70.0ms (1.2%)

prune87.0ms (1.5%)

regimes538.0ms (9.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (38.4%)

Profiling