Details

sample90.0ms

Algorithm

intervals

Results

32.0ms	86×	body	2560	valid
22.0ms	85×	body	1280	valid
11.0ms	300×	body	80	nan
8.0ms	43×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	9×	body	80	valid

simplify100.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	7
7	5002	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

7.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	336	587
1	1261	535
2	5002	531

prune134.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.5b

Counts

73 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow v 2) (pow v 4))
0.0b	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.6b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`associate-r`
3×	`associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-*r/` `associate--l+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `acos-asin` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+ (pow v 2) (pow v 4))
9.0ms	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
9.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series206.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (pow v 2) (pow v 4))
43.0ms	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
91.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	222	434
1	995	393
2	5001	386

prune130.0ms

Filtered

69 candidates to 46 candidates (66.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	69	4	73

Merged error: 0.5b

Counts

73 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
16.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
19.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
4.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify113.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	125	1002
1	427	888
2	2342	844
3	5002	813

prune143.0ms

Filtered

95 candidates to 49 candidates (51.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	90	9	99

Merged error: 0.5b

Counts

99 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)))
1.0b	(pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)
1.0b	(cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
48×	`cbrt-prod`
35×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
22×	`unpow-prod-down` `cube-prod`
21×	`associate-r`
14×	`unswap-sqr`
9×	`pow1`
7×	`add-exp-log`
6×	`associate-l` `add-cbrt-cube`
5×	`sqr-pow`
4×	`add-log-exp`
3×	`cube-mult` `pow-unpow` `pow-pow` `unpow3`
2×	`sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `sqrt-pow2` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 124

Calls

4 calls:

1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
11.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)))
3.0ms	(pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)
3.0ms	(cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3))

series97.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
4.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)))
57.0ms	(pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3)
17.0ms	(cbrt (pow (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) 3))

simplify55.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	234	2030
1	980	1607
2	5001	1494

prune174.0ms

Filtered

136 candidates to 59 candidates (43.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	136	9	145

Merged error: 0.5b

Counts

145 → 9

regimes205.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	6
1	13	6

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	2975×	body	2560	valid
636.0ms	2436×	body	1280	valid
305.0ms	8226×	body	80	nan
254.0ms	1295×	body	640	valid
86.0ms	617×	body	320	valid
45.0ms	458×	body	160	valid
12.0ms	219×	body	80	valid

Details

sample90.0ms

simplify100.0ms

prune2.0ms

localize7.0ms

rewrite16.0ms

series112.0ms

simplify39.0ms

prune134.0ms

localize8.0ms

rewrite27.0ms

series206.0ms

simplify36.0ms

prune130.0ms

localize10.0ms

rewrite12.0ms

series43.0ms

simplify113.0ms

prune143.0ms

localize14.0ms

rewrite25.0ms

series97.0ms

simplify55.0ms

prune174.0ms

regimes205.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling