Details

analyze510.0ms (13.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample35.0ms (1%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	80	valid
1.0ms	12×	body	80	invalid
1.0ms	12×	body	80	nan

simplify229.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (227.0ms)

Iter	Nodes	Cost
0	3532	37
1	3532	37

prune14.0ms (0.4%)

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: 21.1b

Counts

2 → 2

localize23.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 62

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series67.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify59.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4900	1063
1	4900	1063

prune222.0ms (6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Merged error: 5.3b

Counts

76 → 7

localize27.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0b	(* c (/ a b))
5.5b	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
13×	`times-frac` `associate-r`
8×	`add-log-exp`
7×	`pow1`
4×	`sqrt-prod`
3×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `diff-log` `associate-/r/` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `clear-num` `-commutative` `flip-+` `associate-/l*`

Counts

4 → 87

Calls

4 calls:

10.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(* c (/ a b))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series52.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(* c (/ a b))

simplify43.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5085	1233

prune253.0ms (6.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	98	8	106

Merged error: 5.3b

Counts

106 → 8

localize32.0ms (0.9%)

Local error

Found 4 expressions with local error:

22.1b	(cbrt (* c (/ a b)))
22.1b	(cbrt (* c (/ a b)))
22.1b	(cbrt (* c (/ a b)))
25.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*r/` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 45

Calls

4 calls:

6.0ms	(cbrt (* c (/ a b)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (* c (/ a b)))
4.0ms	(cbrt (* c (/ a b)))

series74.0ms (2%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (* c (/ a b)))
19.0ms	(cbrt (* c (/ a b)))
19.0ms	(cbrt (* c (/ a b)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify38.0ms (1%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5057	527

prune146.0ms (4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	57	8	65

Merged error: 5.3b

Counts

65 → 8

localize35.0ms (1%)

Local error

Found 4 expressions with local error:

5.5b	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
9.0b	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
25.9b	(cbrt (- (* b b) (* 4.0 (* a c))))
25.9b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`cbrt-prod`
4×	`pow1` `cbrt-div`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`cbrt-undiv` `pow1/3` `diff-log` `div-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 62

Calls

4 calls:

10.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
4.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series100.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
25.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
16.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))

simplify28.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5080	1498

prune237.0ms (6.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	74	8	82

Merged error: 5.3b

Counts

82 → 8

regimes275.0ms (7.5%)

Accuracy

Total 1.0b remaining (15.1%)

Threshold costs 0b (0%)

bsearch54.0ms (1.5%)

Steps

Iters	Range		Point
6	9.787932035736412e+94	8.940413729942685e+95	2.4627280993291758e+95
9	-5.1924188960394814e+126	-2.9084194526898267e+121	-5.0667631505325645e+124

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	153	121
1	153	121

end0.0ms (0%)

sample1.0s (27.3%)

Algorithm

1×

intervals

Results

699.0ms	8000×	body	80	valid
62.0ms	707×	body	80	nan
33.0ms	391×	body	80	invalid

Details

analyze510.0ms (13.9%)

sample35.0ms (1%)

simplify229.0ms (6.2%)

prune14.0ms (0.4%)

localize23.0ms (0.6%)

rewrite33.0ms (0.9%)

series67.0ms (1.8%)

simplify59.0ms (1.6%)

prune222.0ms (6%)

localize27.0ms (0.7%)

rewrite33.0ms (0.9%)

series52.0ms (1.4%)

simplify43.0ms (1.2%)

prune253.0ms (6.9%)

localize32.0ms (0.9%)

rewrite18.0ms (0.5%)

series74.0ms (2%)

simplify38.0ms (1%)

prune146.0ms (4%)

localize35.0ms (1%)

rewrite24.0ms (0.6%)

series100.0ms (2.7%)

simplify28.0ms (0.8%)

prune237.0ms (6.5%)

regimes275.0ms (7.5%)

bsearch54.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (27.3%)

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