Details

analyze740.0ms (13.3%)

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%	74.9%	25.1%	8
6.2%	68.6%	25.1%	9
7.8%	67.1%	25.1%	10
10.1%	64.7%	25.1%	11
14.8%	47.6%	37.6%	12
15.8%	36.8%	47.4%	13
16.6%	35.1%	48.3%	14

sample51.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	80	valid
9.0ms	162×	body	80	invalid
8.0ms	146×	body	80	nan

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5189	17

prune8.0ms (0.2%)

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: 0.3b

Counts

2 → 1

localize16.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/ (* t t) 2.0)
0.0b	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0)))
0.2b	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-cbrt-cube`
13×	`add-exp-log`
10×	`pow1` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`associate-*l/`
5×	`prod-exp` `cbrt-unprod`
4×	`associate-l` `pow-prod-down`
3×	`times-frac` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `div-exp` `*-commutative` `flip--`
1×	`frac-2neg` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `unswap-sqr`

Counts

3 → 62

Calls

3 calls:

12.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0)))
8.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))
4.0ms	(/ (* t t) 2.0)

series63.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0)))
15.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))
6.0ms	(/ (* t t) 2.0)

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4969	861
1	4969	861

prune197.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 0.0b

Counts

72 → 10

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(* (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (* (cbrt (exp (/ (* t t) 2.0))) (cbrt (exp (/ (* t t) 2.0))))) (cbrt (exp (/ (* t t) 2.0))))
0.0b	(* (cbrt (exp (/ (* t t) 2.0))) (cbrt (exp (/ (* t t) 2.0))))
0.0b	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (* (cbrt (exp (/ (* t t) 2.0))) (cbrt (exp (/ (* t t) 2.0)))))
0.2b	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

rewrite60.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`pow1`
38×	`add-exp-log`
26×	`add-sqr-sqrt`
24×	`pow-prod-down`
23×	`prod-exp` `add-cbrt-cube` `cbrt-unprod`
19×	`cbrt-prod`
17×	`associate-r`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-*l/`
11×	`associate-l`
6×	`pow1/3` `swap-sqr`
5×	`unswap-sqr`
4×	`*-commutative` `add-log-exp`
3×	`flip3--` `flip--`
2×	`pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `sqrt-prod`

Counts

4 → 117

Calls

4 calls:

21.0ms	(* (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (* (cbrt (exp (/ (* t t) 2.0))) (cbrt (exp (/ (* t t) 2.0))))) (cbrt (exp (/ (* t t) 2.0))))
19.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (* (cbrt (exp (/ (* t t) 2.0))) (cbrt (exp (/ (* t t) 2.0)))))
9.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))
8.0ms	(* (cbrt (exp (/ (* t t) 2.0))) (cbrt (exp (/ (* t t) 2.0))))

series167.0ms (3%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (* (cbrt (exp (/ (* t t) 2.0))) (cbrt (exp (/ (* t t) 2.0)))))
45.0ms	(* (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (* (cbrt (exp (/ (* t t) 2.0))) (cbrt (exp (/ (* t t) 2.0))))) (cbrt (exp (/ (* t t) 2.0))))
26.0ms	(* (cbrt (exp (/ (* t t) 2.0))) (cbrt (exp (/ (* t t) 2.0))))
14.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

simplify47.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5007	2080

prune462.0ms (8.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	129	10	139

Merged error: 0.0b

Counts

139 → 10

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp (/ (* t t) 2.0)))
0.0b	(* (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp (/ (* t t) 2.0)) 2/3)) (cbrt (exp (/ (* t t) 2.0))))
0.0b	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp (/ (* t t) 2.0)) 2/3))
0.2b	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log`
26×	`prod-exp`
17×	`associate-r` `add-cbrt-cube`
13×	`add-sqr-sqrt`
12×	`associate-*l/`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`cbrt-unprod`
8×	`pow1`
6×	`cbrt-prod`
5×	`associate-l`
4×	`pow-to-exp` `pow-exp` `add-log-exp`
3×	`unpow-prod-down` `flip3--` `*-commutative` `flip--`
2×	`pow-prod-down`
1×	`pow1/3` `sqrt-prod` `unswap-sqr` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

16.0ms	(* (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp (/ (* t t) 2.0)) 2/3)) (cbrt (exp (/ (* t t) 2.0))))
12.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp (/ (* t t) 2.0)) 2/3))
9.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))
3.0ms	(cbrt (exp (/ (* t t) 2.0)))

series164.0ms (3%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp (/ (* t t) 2.0)) 2/3))
46.0ms	(* (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp (/ (* t t) 2.0)) 2/3)) (cbrt (exp (/ (* t t) 2.0))))
21.0ms	(cbrt (exp (/ (* t t) 2.0)))
14.0ms	(* (- (* x 0.5) y) (sqrt (* z 2.0)))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5060	1574

prune305.0ms (5.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	98	10	108

Merged error: 0.0b

Counts

108 → 10

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/ (* t t) 2.0)
0.0b	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0)) (exp (/ (* t t) 2.0)))
0.2b	(* (- (* x 0.5) y) (sqrt z))
0.5b	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-cbrt-cube`
22×	`add-exp-log`
20×	`pow1`
16×	`add-sqr-sqrt`
15×	`associate-r`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
11×	`prod-exp` `cbrt-unprod`
10×	`pow-prod-down`
7×	`sqrt-prod`
5×	`associate-l`
4×	`add-log-exp`
3×	`flip3--` `times-frac` `associate-/r` `-commutative` `flip--`
2×	`cbrt-undiv` `div-exp` `unswap-sqr`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

14.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0)) (exp (/ (* t t) 2.0)))
9.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0))
9.0ms	(* (- (* x 0.5) y) (sqrt z))
4.0ms	(/ (* t t) 2.0)

series79.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0)) (exp (/ (* t t) 2.0)))
16.0ms	(* (* (- (* x 0.5) y) (sqrt z)) (sqrt 2.0))
11.0ms	(* (- (* x 0.5) y) (sqrt z))
3.0ms	(/ (* t t) 2.0)

simplify42.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5012	1257

prune204.0ms (3.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	105	8	113

Merged error: 0b

Counts

113 → 8

regimes1.0s (18.4%)

Accuracy

Total 0.3b remaining (90.5%)

Threshold costs 0.3b (90.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	27
1	34	27

end0.0ms (0%)

sample1.6s (27.9%)

Algorithm

1×

intervals

Results

452.0ms	8000×	body	80	valid
351.0ms	6199×	body	80	invalid
259.0ms	4560×	body	80	nan

Details

analyze740.0ms (13.3%)

sample51.0ms (0.9%)

simplify86.0ms (1.5%)

prune8.0ms (0.2%)

localize16.0ms (0.3%)

rewrite27.0ms (0.5%)

series63.0ms (1.1%)

simplify60.0ms (1.1%)

prune197.0ms (3.5%)

localize17.0ms (0.3%)

rewrite60.0ms (1.1%)

series167.0ms (3%)

simplify47.0ms (0.8%)

prune462.0ms (8.3%)

localize18.0ms (0.3%)

rewrite42.0ms (0.8%)

series164.0ms (3%)

simplify74.0ms (1.3%)

prune305.0ms (5.5%)

localize14.0ms (0.3%)

rewrite39.0ms (0.7%)

series79.0ms (1.4%)

simplify42.0ms (0.8%)

prune204.0ms (3.7%)

regimes1.0s (18.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.6s (27.9%)

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