Details

sample42.0ms

Algorithm

intervals

Results

11.0ms	203×	body	80	valid
6.0ms	19×	body	2560	valid
5.0ms	20×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	9×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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

Merged error: 11.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	280	888
1	816	840
2	2486	828
3	5001	827

prune209.0ms

Filtered

93 candidates to 71 candidates (23.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	10	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 11.0b

Counts

94 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `prod-exp` `flip-+`
3×	`sqrt-pow1` `associate-r/` `associate-l*`
2×	`pow1/2` `div-exp` `pow-prod-down` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `1-exp` `sum-log` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

3.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
9.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	390	900
1	1684	818
2	5001	784

prune214.0ms

Filtered

100 candidates to 71 candidates (29.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Merged error: 11.0b

Counts

110 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.3b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
23×	`*-un-lft-identity`
22×	`times-frac`
21×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`log-pow` `unswap-sqr`
4×	`exp-prod` `sqrt-div` `prod-exp`
3×	`log-prod` `flip3-+` `associate-l` `flip-+`
2×	`div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
34.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
12.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	399	962
1	1650	851
2	5002	816

prune275.0ms

Filtered

103 candidates to 76 candidates (26.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 11.0b

Counts

115 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

1.8b	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.3b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`log-prod` `log-pow`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `exp-prod`
6×	`add-log-exp`
5×	`add-exp-log` `sqrt-prod`
4×	`add-cbrt-cube`
2×	`flip3-+` `sqrt-div` `rem-log-exp` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 59

Calls

4 calls:

2.0ms	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
33.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
12.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	267	855
1	729	738
2	2550	736
3	5002	735

prune188.0ms

Filtered

71 candidates to 59 candidates (16.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 5.5b

Counts

83 → 8

regimes208.0ms

Accuracy

-10.9% (6.6b remaining)

Error of 13.9b against oracle of 7.4b and baseline of 13.3b

bsearch61.0ms

Steps

Iters	Range		Point
7	-2.450180232760445e-303	-3.4104780537685076e-305	-3.5755809718925854e-305
7	-2.414893472892736e-252	-8.944980550579625e-254	-6.219040641904291e-253

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	46
1	61	46

end0.0ms

sample1.3s

Algorithm

intervals

Results

329.0ms	6055×	body	80	valid
260.0ms	796×	body	2560	valid
171.0ms	622×	body	1280	valid
138.0ms	8000×	pre	80	true
67.0ms	324×	body	640	valid
21.0ms	137×	body	320	valid
7.0ms	66×	body	160	valid

Details

sample42.0ms

simplify8.0ms

prune3.0ms

localize16.0ms

rewrite38.0ms

series64.0ms

simplify73.0ms

prune209.0ms

localize13.0ms

rewrite28.0ms

series64.0ms

simplify44.0ms

prune214.0ms

localize17.0ms

rewrite27.0ms

series63.0ms

simplify43.0ms

prune275.0ms

localize20.0ms

rewrite13.0ms

series94.0ms

simplify68.0ms

prune188.0ms

regimes208.0ms

bsearch61.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling