Details

Time bar (total: 10.0m)

sample63.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
15.0ms236×body80nan

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05017
110817
238917
3176117
4500217

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.0b

Counts
2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (sqrt (+ t a)))
0.3b
(/ 2.0 (* t 3.0))
1.6b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.1b
(/ (* z (sqrt (+ t a))) t)

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
5600×frac-sub
4092×add-sqr-sqrt
3181×*-un-lft-identity
2442×associate-/l*
2267×add-cube-cbrt
2241×associate-*r*
2163×associate-/r*
1900×frac-times
1511×times-frac
1468×flip3-+ flip-+
1365×prod-diff
1354×associate-*l*
1186×associate-*r/
1051×flip3-- flip--
907×sqrt-prod
658×unswap-sqr
414×*-commutative
328×associate--r+
316×distribute-lft-out
268×frac-2neg clear-num
236×sqrt-div
234×associate-/l/
228×difference-of-squares
169×distribute-lft-out--
164×distribute-rgt-in distribute-lft-in
55×fma-neg
50×associate-*l/
30×div-inv
16×add-exp-log add-cbrt-cube
6×pow1 add-log-exp
4×cbrt-undiv expm1-log1p-u div-exp associate--l+ log1p-expm1-u
3×sub-neg prod-exp cbrt-unprod
2×+-commutative
1×diff-log pow-prod-down
Counts
4 → 4536
Calls
4 calls:
7.0ms
(* z (sqrt (+ t a)))
7.0ms
(/ 2.0 (* t 3.0))
282.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
12.0ms
(/ (* z (sqrt (+ t a))) t)

series356.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* z (sqrt (+ t a)))
16.0ms
(/ 2.0 (* t 3.0))
185.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
87.0ms
(/ (* z (sqrt (+ t a))) t)

simplify2.1s

Algorithm
egg-herbie
Counts
4548 → 4548
Iterations

Useful iterations: 0 (123.0ms)

IterNodesCost
09317222027

prune26.5s

Filtered
4548 candidates to 3180 candidates (30.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New454534548
Fresh000
Picked101
Done000
Total454634549

Merged error: 0.0b

Counts
4549 → 3

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt t)
0.6b
(cbrt t)
0.6b
(cbrt t)
1.1b
(fma (/ (* (cbrt z) (cbrt z)) (* (cbrt t) (cbrt t))) (/ (* (cbrt z) (sqrt (+ t a))) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt t)
1.0ms
(cbrt t)
1.0ms
(cbrt t)
1.0ms
(fma (/ (* (cbrt z) (cbrt z)) (* (cbrt t) (cbrt t))) (/ (* (cbrt z) (sqrt (+ t a))) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
189.0ms
(cbrt t)
186.0ms
(cbrt t)
188.0ms
(cbrt t)
466.0ms
(fma (/ (* (cbrt z) (cbrt z)) (* (cbrt t) (cbrt t))) (/ (* (cbrt z) (sqrt (+ t a))) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0185450
1504391
22161378
35001374

prune369.0ms

Filtered
61 candidates to 54 candidates (11.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New61061
Fresh022
Picked011
Done000
Total61364

Merged error: 0.0b

Counts
64 → 3

localize37.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
5.8b
(- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) (/ 2.0 1))))))
5.9b
(/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t)))
22.1b
(/ (- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) (/ 2.0 1)))))) (* (cbrt t) (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite53.0s

Algorithm
rewrite-expression-head
Rules
332414×add-sqr-sqrt
141325×unswap-sqr
117416×associate-*l/
113240×frac-sub
108352×frac-times
107788×associate-*r*
102580×*-un-lft-identity
101965×associate-*l*
96084×associate-*r/
86200×times-frac
85262×flip3-- flip--
63315×cbrt-prod
55455×add-cube-cbrt
49595×prod-diff
47589×associate-/r*
38117×associate-/l*
38104×difference-of-squares
31238×associate-/l/
23679×distribute-lft-out--
22809×swap-sqr
21620×sqrt-prod
15568×distribute-rgt-in distribute-lft-in associate--r+
14215×*-commutative
8318×clear-num
7785×div-sub
6530×frac-2neg
3576×un-div-inv
2812×distribute-lft-out
2330×sqrt-div
1165×flip3-+ flip-+
638×div-inv
577×fma-neg
57×add-cbrt-cube
35×add-exp-log
28×cbrt-unprod
17×cbrt-undiv
13×prod-exp
9×pow1 sub-neg
8×div-exp
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down
2×associate-/r/
1×diff-log
Counts
4 → 127705
Calls
4 calls:
76.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
4.2s
(- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) (/ 2.0 1))))))
71.0ms
(/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t)))
8.7s
(/ (- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) (/ 2.0 1)))))) (* (cbrt t) (* (- a (/ 5.0 6.0)) (* t 3.0))))

series4.8s

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
2.2s
(- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) (/ 2.0 1))))))
316.0ms
(/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t)))
2.2s
(/ (- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) (/ 2.0 1)))))) (* (cbrt t) (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify2.0m

Algorithm
egg-herbie
Counts
127717 → 127717
Iterations

Useful iterations: 0 (6.0s)

IterNodesCost
012557310372966

prune6.6m

Filtered
127717 candidates to 72256 candidates (43.4%)