Details

analyze1.3s (20.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5017	231
0	5	5
1	5	5

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
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample36.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	68×	body	128	nan
1.0ms	28×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	806	21
1	806	21

prune3.0ms (0%)

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

28.3b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 z z) (.f64 t a))
3.9b	(.f64 (.f64 x y) z)
12.0b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
25.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_7277` `add-cbrt-cube_binary64_7275`
11×	`add-sqr-sqrt_binary64_7261`
10×	`*-un-lft-identity_binary64_7239` `pow1_binary64_7300` `add-cube-cbrt_binary64_7274`
9×	`sqrt-prod_binary64_7255`
6×	`add-log-exp_binary64_7278` `associate-/r*_binary64_7183` `cbrt-unprod_binary64_7272` `prod-exp_binary64_7288` `times-frac_binary64_7245`
4×	`sqrt-div_binary64_7256`
3×	`flip3--_binary64_7243` `pow-prod-down_binary64_7310` `flip--_binary64_7214` `cbrt-undiv_binary64_7273` `div-exp_binary64_7290` `associate-r_binary64_7179`
2×	`associate-/r/_binary64_7185`
1×	`pow1/2_binary64_7319` `rem-sqrt-square_binary64_7252` `frac-2neg_binary64_7250` `-commutative_binary64_7170` `associate-/l_binary64_7184` `div-inv_binary64_7236` `cancel-sign-sub-inv_binary64_7205` `sqrt-pow1_binary64_7257` `sub-neg_binary64_7232` `diff-log_binary64_7331` `clear-num_binary64_7238` `associate-l_binary64_7180`

Counts

4 → 76

Calls

4 calls:

16.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 (.f64 x y) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series233.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
56.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
27.0ms	(-.f64 (.f64 z z) (.f64 t a))
26.0ms	(.f64 (.f64 x y) z)

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5138	1472

prune99.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Error

3.3b

Counts

89 → 10

Compiler

Compiled 1813 to 379 computations (79.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.8b	(-.f64 (.f64 z z) (.f64 t a))
3.3b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
25.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_7245`
34×	`add-sqr-sqrt_binary64_7261`
33×	`*-un-lft-identity_binary64_7239` `add-cube-cbrt_binary64_7274`
24×	`sqrt-prod_binary64_7255` `associate-r_binary64_7179`
18×	`add-exp-log_binary64_7277` `add-cbrt-cube_binary64_7275`
10×	`pow1_binary64_7300`
6×	`add-log-exp_binary64_7278` `associate-/r*_binary64_7183` `cbrt-unprod_binary64_7272` `prod-exp_binary64_7288` `sqrt-div_binary64_7256`
4×	`flip3--_binary64_7243` `flip--_binary64_7214` `associate-/r/_binary64_7185`
3×	`pow-prod-down_binary64_7310` `associate-/l*_binary64_7184` `cbrt-undiv_binary64_7273` `div-exp_binary64_7290`
2×	`div-inv_binary64_7236`
1×	`pow1/2_binary64_7319` `associate-r/_binary64_7181` `rem-sqrt-square_binary64_7252` `frac-2neg_binary64_7250` `-commutative_binary64_7170` `cancel-sign-sub-inv_binary64_7205` `sqrt-pow1_binary64_7257` `sub-neg_binary64_7232` `diff-log_binary64_7331` `clear-num_binary64_7238` `associate-l_binary64_7180`

Counts

4 → 112

Calls

4 calls:

15.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series247.0ms (4%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
57.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
41.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
28.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5326	2521

prune95.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	126	8	134

Error

3.3b

Counts

134 → 8

Compiler

Compiled 2779 to 483 computations (82.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 z z) (.f64 t a))
1.3b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
2.8b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
25.8b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_7261`
25×	`associate-r_binary64_7179`
20×	`*-un-lft-identity_binary64_7239` `times-frac_binary64_7245` `add-cube-cbrt_binary64_7274`
18×	`add-exp-log_binary64_7277` `add-cbrt-cube_binary64_7275`
13×	`sqrt-prod_binary64_7255`
12×	`pow1_binary64_7300`
7×	`cbrt-unprod_binary64_7272` `prod-exp_binary64_7288`
6×	`add-log-exp_binary64_7278` `associate-l_binary64_7180`
4×	`pow-prod-down_binary64_7310` `sqrt-div_binary64_7256`
3×	`associate-*r/_binary64_7181` `flip3--_binary64_7243` `flip--_binary64_7214` `unswap-sqr_binary64_7207`
2×	`*-commutative_binary64_7170` `associate-/r/_binary64_7185` `cbrt-undiv_binary64_7273` `div-exp_binary64_7290`
1×	`pow1/2_binary64_7319` `rem-sqrt-square_binary64_7252` `div-inv_binary64_7236` `cancel-sign-sub-inv_binary64_7205` `sqrt-pow1_binary64_7257` `sub-neg_binary64_7232` `diff-log_binary64_7331`

Counts

4 → 92

Calls

4 calls:

17.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
12.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series280.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
77.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
51.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
26.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5059	1897

prune79.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	104	8	112

Error

3.3b

Counts

112 → 8

Compiler

Compiled 2216 to 468 computations (78.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.5b	(/.f64 (.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) z) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
9.3b	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) z)
26.6b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
26.6b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64_7277` `add-cbrt-cube_binary64_7275`
17×	`add-sqr-sqrt_binary64_7261`
15×	`*-un-lft-identity_binary64_7239` `add-cube-cbrt_binary64_7274`
12×	`sqrt-prod_binary64_7255` `cbrt-prod_binary64_7270` `times-frac_binary64_7245`
9×	`associate-/r*_binary64_7183`
8×	`cbrt-unprod_binary64_7272` `prod-exp_binary64_7288` `cbrt-undiv_binary64_7273` `div-exp_binary64_7290`
7×	`associate-l_binary64_7180`
6×	`cbrt-div_binary64_7271` `pow1_binary64_7300`
4×	`add-log-exp_binary64_7278`
3×	`flip3--_binary64_7243` `flip--_binary64_7214` `associate-r_binary64_7179`
2×	`associate-*l/_binary64_7182` `pow1/3_binary64_7321` `associate-/r/_binary64_7185` `sqrt-div_binary64_7256` `div-inv_binary64_7236`
1×	`pow-prod-down_binary64_7310` `frac-2neg_binary64_7250` `unswap-sqr_binary64_7207` `associate-/l/_binary64_7186` `-commutative_binary64_7170` `associate-/l_binary64_7184` `clear-num_binary64_7238`

Counts

4 → 93

Calls

4 calls:

13.0ms	(/.f64 (.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) z) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
7.0ms	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) z)
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series655.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

361.0ms	(/.f64 (.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) z) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
133.0ms	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) z)
83.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
78.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4973	3179
1	4973	3179

prune97.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	104	9	113

Error

3.3b

Counts

113 → 9

Compiler

Compiled 3378 to 450 computations (86.7% saved)

regimes871.0ms (14.1%)

Accuracy

Total 3.3b remaining (49%)

Threshold costs 0b (0%)

Compiler

Compiled 6056 to 4110 computations (32.1% saved)

bsearch52.0ms (0.8%)

Steps

Iters	Range		Point
10	2.6106127917356385e+148	7.44658992833752e+159	6.085591062768923e+152
6	-1.1212657813029003e+98	-9.665978320946834e+96	-1.1025272260676565e+98

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	43
1	70	43

Compiler

Compiled 116 to 76 computations (34.5% saved)

end0.0ms (0%)

sample1.6s (26.4%)

Algorithm

1×

intervals

Results

436.0ms	8000×	body	128	valid
108.0ms	2283×	body	128	nan
50.0ms	902×	body	128	invalid

Compiler

Compiled 744 to 503 computations (32.4% saved)

Details

analyze1.3s (20.4%)

sample36.0ms (0.6%)

simplify55.0ms (0.9%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite35.0ms (0.6%)

series233.0ms (3.8%)

simplify54.0ms (0.9%)

prune99.0ms (1.6%)

localize10.0ms (0.2%)

rewrite40.0ms (0.7%)

series247.0ms (4%)

simplify80.0ms (1.3%)

prune95.0ms (1.5%)

localize10.0ms (0.2%)

rewrite45.0ms (0.7%)

series280.0ms (4.5%)

simplify59.0ms (1%)

prune79.0ms (1.3%)

localize14.0ms (0.2%)

rewrite38.0ms (0.6%)

series655.0ms (10.6%)

simplify68.0ms (1.1%)

prune97.0ms (1.6%)

regimes871.0ms (14.1%)

bsearch52.0ms (0.8%)

simplify11.0ms (0.2%)

end0.0ms (0%)

sample1.6s (26.4%)

Profiling